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Topic: Induced representation

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	Induced representation - Wikipedia, the free encyclopedia
		The theorem states that, given representations ρ of G and σ of H, the space of G-intertwining maps from ρ to Ind(σ) has the same dimension as that of the H-intertwining maps from Res(ρ) to σ.
		There is a third and classical approach, of simply writing down the character (trace) of the induced representation, in terms of conjugation in G of elements g into H.
		In the case of unitary representations of locally compact groups, the induction construction can be formulated in terms of systems of imprimitivity.
	en.wikipedia.org /wiki/Induced_representation (756 words)

	[No title]
		A representation of a group means a homomorphism of G to a "known" group.
		In the case of permutation representations, given H --> Sym(S) (that is, H is viewed as permuting a (usu.
		Now, in the case of linear representations, the "induced representation" is defined in a similar way, but the goal is to find another _vector space_ on which G can act.
	www.math.niu.edu /~rusin/known-math/95/induced.rep (902 words)

	[No title]
		When V is an induced representation from some subgroup K to G, which we realize geometrically as the space of functions on G/K, the corresponding algebra is essentially what is known as the Hecke algebra H(G;K).
		An element of the principal series corresponds to the induced representation from the upper-triangular subgroup of the character which assigns to an upper diagonal matrix with a, 1/a on the diagonal the number x(a), where x is a character on the real line.
		Inducing partway from N to B (all upper-triangulars) it follows that U is the direct integral of ALL members of the principal series..thus indeed giving all the continuous spectrum of V(J) through intertwiners.
	www.ma.utexas.edu /~benzvi/math/Langlands2 (1321 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		Hence Rieffel's far-reaching operator-algebraic generalization of the notion of an induced representation is seen to be the exact quantum counterpart of the classical idea of symplectic reduction, with imprimitivity bimodules and strong Morita equivalence of $C^*$-algebras falling in the right place.
		While a direct quantization of the reduced symplectic manifolds and concordant induced representations of Poisson algebras may be possible in certain examples, a systematic approach intending to mimic the classical reduction/induction procedure in some quantum fashion ought to start from a quantization of the `unconstrained' system.
		A co-adjoint orbit $\O\subset \h^$ is then analogous to an irreducible unitary representation* $\plg$, and the Marsden-Weinstein reduced space $J^{-1}(\O)/H\equiv (T^G)^{\O}$, carrying the induced* action $\pi^{\O}$ of $\cin(\g^)$, is the symplectic counterpart of the Hilbert space $\hug$ carrying the induced* representation $\pug$ of $G$ (or $C^*(G)$).
	www.ma.utexas.edu /mp_arc/papers/93-289 (9809 words)

	MTH-3E20 : Representation Theory
		Representation Theory demonstrates the enormous power of linear algebra and builds upon what students have learned at level 1 and 2 in Pure Mathematics I and II and Algebra I and II.
		The idea of equivalence of representations is crucial for the theory, although initially quite difficult to grasp.
		The theory of induced representations introduces students to efficient and practical methods of constructing and analysing representations.
	www.mth.uea.ac.uk /maths/syllabuses/0001/3E2001.html (534 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-11-01)
		Unitary representation) of nilpotent Lie groups was developed using the orbit method, and it has been shown that this method can also be used for other groups (see [1]).
		The solution of basic problems in the theory of representations using the orbit method is achieved in the following way (see [2]).
		This formula is correct for nilpotent groups, solvable groups of type 1, compact groups, discrete series of representations of semi-simple real groups, and principal series of representations of complex semi-simple groups.
	eom.springer.de /O/o070020.htm (804 words)

	Applying an Integrated Model to the Evaluation of Travel Demand Management Policies in the Sacramento Region (Site not responding. Last check: 2007-11-01)
		In Chapter Three, (Representation of Induced Travel in the Sacramento MEPLAN Model) sensitivity tests were conducted to evaluate the potential importance of the induced travel effects represented in the current version of the Sacramento MEPLAN model.
		The induced travel hypothesis is grounded in economic theory and predicts that an increase in roadway supply reduces the time cost of travel and thus increases the quantity of travel demanded (or vehicle travel).
		The representation of induced travel effects in travel demand modeling is critical to the accurate evaluation of highway and transit alternatives.
	transweb.sjsu.edu /mtiportal/research/publications/documents/SAC.htm (13301 words)

	[No title]
		To me the induced representation of G is an action of G on either the set (G/H)xV or the vector space F[G/H]\tensor V, where F[G/H] is the vector space spanned by G/H. I'm not sure how you intend these to be equivalent to an action of G on GxV.
		The representations conjugate to f: H --> Aut(H) are f o g where g: H --> H is conjugation by an element of N(H).
		In general there is a "degree of inertia" or something, call it e, associated to an N(H)-invariant representation f such that the direct sum of e copies of f is the restriction of a rep of N(H).
	www.math.niu.edu /~rusin/known-math/95/extend.rep (2355 words)

	Transweb - Mineta Transportation Institute (Site not responding. Last check: 2007-11-01)
		Induced demand analysis shows that new transportation capacity produced absolute percent changes in the zero to 25 percent range for 75 and 85 percent of zones for households and residential land, respectively, and in the 26 to 50 percent range for 30 and 35 percent of zones for employment and nonresidential land, respectively.
		Relative to estimated actual induced travel, the model overestimated the number of zones with smaller changes and underestimated the number of zones with larger changes (1 to 19 percent).
		The share of significant model-induced employment and nonresidential land (greater than zonal absolute model error) relative to the regional total was 14 and 21 percent, respectively; 3 percent for households; and 1 percent for residential land.
	transweb.sjsu.edu /mtiportal/research/publications/summary/0502.html (747 words)

	Rupert Venzke - DIMACS REU Program (Summer 2002)
		A representation of a Lie Group G is basically a structure-preserving map from G into GL(n), the general linear group of n
		Specifically, a character χ on the group G, with representation φ, is the map χ: G → F defined by χ(g) = Trace(φ(g)).
		A representation of a Lie Group is called irreducible if its corresponding group-ring module has no non-trivial submodules under the action of FG.
	dimacs.rutgers.edu /~rvenzke (807 words)

	Innovative Mobility Research Group
		This has brought renewed attention to the representation of induced travel in regional land use and travel demand models.
		In addition, these studies have conducted sensitivity tests, by turning on and off model components, to isolate the relative contribution with respect to the models' representation of induced travel.
		If induced travel is not represented in travel and land use models, then the need for, and the benefit of, a highway project will tend to be overstated (e.g., 16 to 236 percent of vehicle hours traveled), and negative environmental effects will be overstated (e.g., 72 to 192 percent of NOX vehicle emissions).
	database.path.berkeley.edu /imr/index.cgi?reqtype=displayrecord&record=21&range=0 (205 words)

	Sally, Tadic: Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$
		Sally, Tadic: Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$
		Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$.
		[Z1] Zelevinsky, A.V. Induced representations of reductive p-adic groups II, On irreducible representations of GL(n), Ann.
	www.numdam.org /item?id=MSMF_1993_2_52__75_0 (403 words)

	[No title]
		It is known that every complex irreducible representation of G can be induced from a 1-dimensional representation of a suitable subgroup, however, this fact alone is insufficient for the purpose of classifying such representations.
		It classifies irreducible representations of G in terms of "coadjoint orbits", which are orbits of the action of G on a certain abelian group naturally associated to G. On the other hand, there is a geometric setting.
		Objects of C are finite-dimensional supervector spaces, Hom(U,V) is the derived category of finite-dimensional representations of the free algebra generated by the usual hom-space Hom(V,U).
	www.math.uchicago.edu /seminars/geometric_langlands.html (5218 words)

	Math Forum Discussions (Site not responding. Last check: 2007-11-01)
		Let f be an irreducible representation of H. Let t be an automorphism of H coming from G - H (H is normal so conjugation of H is an automorphism).
		t acts on the irreducible representations of H by t*g(x) = g(t(x)) = g(txt^(-1)).
		Ind_H^G (f) restricted to H is the direct sum of the representations f
	mathforum.org /kb/thread.jspa?threadID=1339385&messageID=4488889 (291 words)

	Representation Theory of Groups - Teoria della Rappresentazione dei Gruppi (Site not responding. Last check: 2007-11-01)
		Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras.
		The Tits representation of Coxeter groups is faithful (Agrigoroaiei);
		The Grothendieck group of the category of representations of the symmetric group and its Hopf algebra structure (Shanwen Wang);
	www.math.unipd.it /~carnoval/rappre.html (391 words)

	Bernstein, Zelevinsky: Induced representations of reductive ${\germ p}$-adic groups. I (Site not responding. Last check: 2007-11-01)
		Bernstein, I. Zelevinsky, A. Induced representations of reductive ${\germ p}$-adic groups.
		ZELEVINSKY, Representations of the group GL (n, F), where F is a local Non-Archimedean Field, (Uspekhi Mat.
		KAJDAN, On Representations of the Group GL (n, K), where K is a local Field (Funkt.
	www.numdam.org /item?id=ASENS_1977_4_10_4_441_0 (190 words)

	Stimulation-Induced Within-Representation and Across-Representation Plasticity in Human Motor Cortex -- Ziemann et al. ...
		The human motor cortex contains a dynamic and distributed network of motor representations.
		on the motor output from the upper arm representation.
		and arm/hand representations induced a prolonged (> 60 min) within-representation
	www.jneurosci.org /cgi/content/abstract/22/13/5563 (450 words)

	Proceedings of the American Mathematical Society
		Abstract: This paper studies the behavior of the associated variety under induction from real parabolic subgroups.
		We derive a formula for the associated variety of an induced module which is analogous to the formula for the wave front set of a derived functor module obtained by Barbasch and Vogan.
		D. Barbasch and D. Vogan, Weyl Group Representations and Nilpotent Orbits, Representation Theory of Reductive Groups (P.C. Trombi, eds.), Birkhäuser-Boston, 1983, pp.
	www.mathaware.org /proc/1999-127-01/S0002-9939-99-04482-2/home.html (266 words)

	MedlinePlus Medical Encyclopedia: Diaper dermatitis - irritant-induced
		A licensed physician should be consulted for diagnosis and treatment of any and all medical conditions.
		Adam makes no representation or warranty regarding the accuracy, reliability, completeness, currentness, or timeliness of the content, text or graphics.
		Links to other sites are provided for information only -- they do not constitute endorsements of those other sites.
	www.nlm.nih.gov /medlineplus/ency/article/000962.htm (278 words)

	Brainstorms: Eric Anderson: Bits, Bytes and Biology: What Evolutionary Algorithms (Don’t) Teach...
		Were the fitness landscape a "flat plain," as Anderson claims Darwin assumed, evolution by natural selection would not happen; only neutral drift would occur.
		A fitness landscape is a topographical representation induced by an evolutionary operator given a fitness function.
		For a given fitness function, each evolutionary operator (three such operators in the Avida program are substitution mutation, deletion mutation, and insertion mutation) induces a different fitness landscape.
	www.iscid.org /boards/ubb-get_topic-f-6-t-000557.html (2721 words)

	Representation of Crystallographic Space Groups; Irreducible Representations, Induced Representation and ...
		Representation of Crystallographic Space Groups; Irreducible Representations, Induced Representation and Corepresentations...
		Home > Books > Nonfiction > Art, Science, History and More > Science > Crystallography
		Representation of Crystallographic Space Groups; Irreducible Representations, Induced Representation and Corepresentations...: Product details
	shopping.msn.com /specs/shp/?itemId=1570433 (50 words)

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