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Topic: Intertwiner

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	Intertwiner
		In mathematical representation theory, an intertwining map or intertwiner for representations of a group G over a field K is the same thing as a module homomorphism of K[G]-modules, where K[G] is the group ring of G.
		Under some conditions, if ρ and σ are both irreducible representations, then an intertwiner (other than the zero map) only exists if the two representations are equivalent (that is, are isomorphic as modules).
		As as consequence, in important cases the construction of an intertwiner is enough to show the representations are effectively the same.
	www.teachersparadise.com /ency/en/wikipedia/i/in/intertwiner.html (258 words)

	HUSH INTERTWINED LYRIC SOUND WE - we sound intertwined, we lyric hush, hush we sound lyric, lyric we hush, hush lyric ... (Site not responding. Last check: 2007-10-20)
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	aawg.starcd.biz (876 words)

	Equivariant - Wikipedia, the free encyclopedia
		Thus an intertwiner is an equivariant map in the special case of two linear representations/actions.
		Alternatively, an intertwiner for representations of G over a field K is the same thing as a module homomorphism of K[G]-modules, where K[G] is the group ring of G.
		Under some conditions, if X and Y are both irreducible representations, then an intertwiner (other than the zero map) only exists if the two representations are equivalent (that is, are isomorphic as modules).
	en.wikipedia.org /wiki/Intertwiner (546 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		In 4 JOHN C. this modified intertwiner we use a dotted line to indicate the splitting of incident edges into `incoming' and `outgoing' pairs: j1 j2 j1 j2 j1 j2 o o X..o....
		For each edge in the spin foam (corresponding to a 3- simplex in the simplicial complex) there are exactly four faces having it in their boundary (corresponding to the four triangles in the 3-simplex).
		Because the associated Barrett- Crane intertwiner is nonzero, Lemma 1 shows that the sum of the spins on these four faces is an integer.
	jdc.math.uwo.ca /papers/positivity.txt (4843 words)

	[No title]
		He only considers spin networks dual to the triangulation, that is, spin networks having one vertex in the middle of each tetrahedron and one edge intersecting each triangular face.
		In such a spin network there are 4 edges meeting at each vertex, and the vertex is labelled with an intertwiner of the form f: j1 tensor j2 -> j3 tensor j4 where j1,...,j4 are the spins on these edges.
		So we get a basis of intertwining operators: f: j1 tensor j2 -> j3 tensor j4 by picking one factoring through each representation j5: j1 tensor j2 -> j5 -> j3 tensor j4 where: a) j1 + j2 + j5 is an integer and j1 - j2
	math.ucr.edu /home/baez/twf_ascii/week110 (1330 words)

	Department of Mathematics (Site not responding. Last check: 2007-10-20)
		We show how intertwiners of tensor product representations of these algebras lead to solutions of the reflection equation.
		Intertwining property of reflection matrices and affine Toda field theory with a boundary
		The most practical way to find spectral parameter dependent R-matrices (solutions of the Yang Baxter equation RRR=RRR) is to impose that R is an intertwiner for a tensor product representation of a quantum affine algebra.
	maths.york.ac.uk /www/PhysicsDeliusTalks (1389 words)

	Department of Mathematical Sciences : Research Seminar Series - Durham University (Site not responding. Last check: 2007-10-20)
		Three mighty weapons did he use - the Q operator - the trick of inversion - and the `intertwiner'.
		I shall describe its role in producing new and exact expressions for correlation functions of the 8-vertex model and its fusion brethren, and will show how a key object, the tail operator, is constructed in terms of it.
		I will opine on how the intertwiner may be related to the twist of Drinfeld.
	www.dur.ac.uk /mathematical.sciences/events/seminars/?seminar=320 (236 words)

	Amazon.com: "intertwiner spaces": Key Phrase page (Site not responding. Last check: 2007-10-20)
		See all pages with references to intertwiner spaces.
		as well as for more general "intertwiner spaces" in the sense of [33].
		Remark 4.23 (Classical intertwiner spaces) As a consequence of (59),...
	www.amazon.com /phrase/intertwiner-spaces (556 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Section 2 is indeed devoted to the construction of a global conjugate charge for a superselection sector $\r$ with finite statistics, a key point relevant in itself, previously an assumption in the related literature.
		In the irreducible case $\bar\r$ is characterized by by the existence of an isometry $V_I\in\A(I)$ that intertwines the identity and $\bar\r\r_{\A(I)}$.
		Their intertwiner space is defined by $$ (\r_1,\r_2)= \{T\in{\cal B}: \r_2(x)T=T\r_1(x),\ x\in{\cal B}\}.\eqno(2.7) $$ In case ${\cal B} =\ua$, $\r_i$ localized in the interval $I_i$ and $T\in (\r_1,\r_2)$, then $\pi_0(T)$ is an intertwiner between the representations $\pi_0\cdot\r_i$.
	www.ma.utexas.edu /mp_arc/html/papers/95-215 (10154 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		A spin foam is a 2-dimensional analogue of a Feynman diagram.
		The Barrett-Crane intertwiner in equation (3) is not normalized; instead, its inner product with itself is j1___________________________________ ________________________________________________________* ____j _________________________________________________________ _____2_____________________________________@ o_________________________________________________________ ___________________________________________@ _________________________________________________________ _________j_________________________________@ ________________________________________________________ *__ 3 j4 so to normalize it we must divide by the square root of this quantity.
		However, since each Barrett-Crane intertwiner in the 10j symbols appears twice in the formula for the Z(F) _ once for each of the two 4-simplices incident to a given 3-simplex _ we obtain a factor of ______1______ j1(e)___________________________________________, _________________________________________________________* ________________________j2(e) __________________________________________________________ ___________________________________________@ o__________________________________________________________ ___________________________________________@ __________________________________________________________ ___________________________________________@ ________________________________________________________ *_____________________________j3(e) j4(e) which gives the edge amplitude A(e).
	jdc.math.uwo.ca /papers/foam4.txt (9236 words)

	Category theory for physicists
		there is a category whose objects are reps of G and whose >>>>morphisms are intertwiners.
		There is a trivial rep of each dimension, but NONE of them >>are isomorphic to each other, because you can't set up an invertible >>linear map between vector spaces of different dimensions.
		And as such, they've gotta be morphisms >in Vect, which are linear.
	www.lns.cornell.edu /spr/2000-10/msg0028587.html (726 words)

	PlanetPhysics: Fermion
		And I replied: "I guess that's what the math gods are trying to tell us!"
		Let's say a unitary rep H of a group G is "real" if it has a conjugate-linear intertwiner j: H -> H with j2 = 1, and let's say it's "quaternionic" if it has one with j2 = -1.
		By this definition, it's clear that if we tensor two quaternionic representations of a group we get a real one.
	planetphysics.org /encyclopedia/Fermion.html (301 words)

	Intuitive content of Loop Gravity--Rovelli's program
		The volume of an object is proportional to the number of nodes of the graph thatr are inside the object.
		Spin networks are used in the canonical approach to quantum gravity, but another approach, the sum-over-histories approach, has adopted a particular version of them, called spin foams, that are cell complexes.
		The intertwiner functions are like fl boxes - deterministically relating spin reps in to spin reps out.
	www.physicsforums.com /showthread.php?t=7245 (3621 words)

	Abstract 1409 (Site not responding. Last check: 2007-10-20)
		More generally, we prove that the intertwiner space $(X_1 \times_{P} \overline{X_{2}})/\gm$ between two Hamiltonian $\gm$-spaces $X_1$ and $X_2$ is a symplectic manifold (whenever it is a smooth manifold); (3) Study Morita equivalence of quasi-symplectic groupoids.
		% in the sense that there is a bijection between their Hamiltonian spaces; Moreover the intertwiner space $(X_1 \times_{P} \overline{X_{2}})/\gm$ is independent of the Morita equivalence.
		As a result, we recover various well-known results concerning equivalence of momentum maps including the Alekseev-Ginzburg-Weinstein linearization theorem and the Alekseev--Malkin--Meinrenken equivalence theorem between quasi-Hamiltonian spaces and Hamiltonian loop group spaces.
	www.esi.ac.at /Abstracts/abs1409.html (218 words)

	week 110
		I should note that the spin networks appearing in the loop representation are different from those Penrose considered, in two important ways.
		First, they can have more than 3 edges meeting at a vertex, and the vertices must be labelled by "intertwining operators", or "intertwiners" for short.
		This is a concept coming from group representation theory; as described in "week109", what we've been calling "spins" are really irreducible representations of SU(2).
	math.ucr.edu /home/baez/week110.html (2198 words)

	Re: Spin foams and gauge theories
		(where an intertwiner f satisfies S(g)f = f R(g), for two representations S and R, for all g in G.) >Paul wrote: >>The zero-dim vector space...(and its one morphism, the identity) >>...Looks like it's isomorphic to >>the identity rep. on a 1-D space, AND a 2-D space, ad nauseum!
		So, the intertwiners have to be linear transformations on the vector spaces?!
		were mentioned, and the intertwiner definition sorta makes you want to draw a commutative diagram...
	www.lns.cornell.edu /spr/2000-10/msg0028558.html (593 words)

	IngentaConnect Massless Relativistic Wave Equations and Quantum Field Theory (Site not responding. Last check: 2007-10-20)
		They are characterized by invariant (and in contrast with the massive case non reducing) one-dimensional projections.
		The definition of one-particle Hilbert space structure that specifies the quantum field uses distinguished elements of the intertwiner space between <EquationSource Format="TEX"><![CDATA[ $$ {mathcal E}(2) $$ ]]></EquationSource> (the two-fold cover of the 2-dimensional Euclidean group) and <EquationSource Format="TEX"><![CDATA[ $$ overline{{mathcal E}(2)}.
		We conclude with a brief comparison between the free nets constructed in Section 3 and a recent alternative construction that uses the notion of modular localization.
	www.ingentaconnect.com /content/klu/23/2004/00000005/00000004/art00001 (284 words)

	Real representation - Wikipedia, the free encyclopedia
		For the former case, the trivial rep could either lie in the symmetric product, or the antisymmetric product.
		Putting all of this together, for an irrep, the second Frobenius-Schur indicator is zero if the irrep isn't self-dual, 1 if it's self-dual and there's a nonzero symmetric intertwiner from
		to the trivial rep and -1 if it's self-dual and there's a nonzero antisymmetric intertwiner from
	en.wikipedia.org /wiki/Real_representation (672 words)

	DPG Tagungen - 1998 - Sitzung MP 2
		The associated Hilbert spaces carry charged representations of the observable algebra, the global transfer matrix and a unitary implementation of the group of spatial lattice translations.
		We prove that for coinciding total charges these representations are dynamically equivalent and we construct a local intertwiner connection depending on a path in the space of charge distributions.
		The holonomy of this connection is given by Z
	www.dpg-tagungen.de /archive/1998/mp_2.html (508 words)

	Topics: Spin Networks
		of SU(2), and vertices n by intertwiners; In the connection rep, spin network states are
		Deformed: Edges of spin networks are enlarged to ribbons or tubes, so the network becomes a tubular, genus-g manifold, decomposable into trinions, separated by circles; Each circle is labeled by a rep of SU(2)
		, each trinion by an intertwiner; Motivation are inclusion of cc, symmetries.
	www.phy.olemiss.edu /~luca/Topics/qg/spin_networks.html (355 words)

	Pearls Plus Freshwater Pearl Pictures - Bridal Romance
		Use the pearl jewellery pieces to enhance your total look or that of your bridesmaids.
		Hair Ornaments There are also freshwater pearl and Swarovski crystal Bobby pins/hair grips/combs plus a pearl and crystal Lariat Intertwiner Strand for dressing bridal hairstyles here.
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	www.pearlsplus.co.uk /bridal_jewellery/freshwater_pearls_bridal_1.htm (450 words)

	First Kansas, now Georgia. [Archive] - Fantasy Sports Wire Forums
		Like I said are we going to bring the bible into our physics classes and chemistry classes?
		This is nothing but a lawsuit waiting to happen because it is so obviously intertwiner with religion.
		Since when did a theory become fact...unless it is a zeppyfact:dunno:
	sportsforum.ws /archive/index.php/t-46633.html (679 words)

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