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	Adjoint representation - Wikipedia, the free encyclopedia
		In mathematics, the adjoint representation (or adjoint action) of a Lie group G is the natural representation of G on its own Lie algebra.
		This representation is the linearized version of the action of G on itself by conjugation.
		The representation is equivalent to that given by the action of G by linear substitution on the space of binary (i.e., 2 variable) quadratic forms.
	en.wikipedia.org /wiki/Adjoint_representation (608 words)

	[No title]
		$L(\xi \nu, \nu ^{-1/2}\pi _{2}))$ of the induced representation $\xi \nu \rtimes \nu ^{-1/2}\pi _{2}$ of $H$, where $\pi _{2}$ is a cuspidal $($irreducible$)$ representation of $\GL (2,F)$ with central character $\xi \neq 1=\xi ^{2}$ and $\xi \pi _{2}=\pi _{2}$, $\lambda $-lifts to the square integrable $($resp.
		The [quasi-]packet $\{\pi _{H}\}$ of an automorphic representation $\pi _{H}$ is defined by the local [quasi-]packets $\{\pi _{Hv}\}$ of the components $\pi _{Hv}$ of $\pi _{H}$ at almost all places.
		A discrete spectrum representation $\pi _{H}$ with component $L(\nu _{v}\xi _{v}, \nu _{v}^{-1/2}\pi _{2v})$ (whose packet consists of itself), where $\pi _{2v}$ is a cuspidal representation with central character $\xi _{v}\neq 1=\xi _{v}^{2}$ and $\xi _{v}\pi _{2v}=\pi _{2v}$, is in the packet of $L(\nu \xi,\nu ^{-1/2}\pi _{2})$.
	www.univie.ac.at /EMIS/journals/ERA-AMS/2004-01-005/2004-01-005.tex.html (4854 words)

	Adjoint representation - TheBestLinks.com - Determinant, Group representation, Group action, Identity element, ... (Site not responding. Last check: 2007-10-02)
		The adjoint representation of a Lie group G is the linearized version of the action of G on itself by conjugation.
		Any Lie group is a representation of itself (via $h\rightarrow ghg^{-1}) and the tangent space is mapped to itself by the group action.$
		According to the philosophy in representation theory known as the orbit method, the irreducible representations of a Lie group G should be indexed in some way by its co-adjoint orbits.
	www.thebestlinks.com /Adjoint_representation.html (422 words)

	THE MEANING OF "TENSOR"
		The Representation Problem The representation problem applies to a particular algebraic structure in a given category, which is to say, to each and every member of the appropriate category.
		A representation of an abstract algebraic structure is a structure preserving homomorphism from the abstract structure into an algebra of matrices.
		Since one can generate all structures or representations from the irreducible ones, isolating the subcategory of irreducible elements is enough to generate the category by the specified means through which irreducibility is defined, and so studying the irreducibles makes either the structure problem or the representation problem easier.
	graham.main.nc.us /~bhammel/MATH/tensor.html (1952 words)

	Crystal page (Site not responding. Last check: 2007-10-02)
		This is not the place for an exposition of representation theory, Lie algebras, or crystal graphs.
		An irreducible representation is denoted by its highest dominant weight vector, written as a linear combination of the ei's.
		For example, the identity representation of A3 is denoted e1 and its contragredient is denoted by e1+e2+e3.
	web.usna.navy.mil /~wdj/crystal.htm (1093 words)

	Predmety - Predmety
		A basic course of the representation theory, which is one of important and powerful theories in mathematics and physics of the 20th century.
		Irreducible representations of simple Lie algebras (classification of representations of sl(2,C), Cartan subalgebras, roots, positive roots, simple roots, weights, weight lattice, Weyl chambers, dominant weights, fundamental weights).
		Classification of irreducible representations of four classical series, construction of fundamental representations, spinor representations,.
	www.mff.cuni.cz /vnitro/is/sis/predmety/kod.php?kod=ALG018 (213 words)

	papers
		Under mild hypotheses (we assume neither that the group is connected, nor that the underlying field has characteristic zero), we describe an explicit region on which the local character expansion is valid.
		Abstract: For a certain class of locally profinite groups, we show that an irreducible smooth discrete series representation is necessarily supercuspidal and, more strongly, can be obtained by induction from a linear character of a suitable open and compact modulo center subgroup.
		Consider the category of smooth (complex) representations of G in which a (fixed) closed cocompact subgroup of the centre acts by a (fixed) character.
	www.math.uakron.edu /~adler/papers (920 words)

	Citebase - Duality for admissible locally analytic representations (Site not responding. Last check: 2007-10-02)
		We study the problem of constructing a contragredient functor on the category of admissible locally analytic representations of a p-adic analytic group G. naive contragredient does not exist.
		On the subcategory corresponding to complexes of smooth representations, this functor induces the usual smooth contragredient (with a degree shift).
		Citation coverage and analysis is incomplete and hit coverage and analysis is both incomplete and noisy.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0403498 (433 words)

	International Journal of Mathematics and Mathematical Sciences (Site not responding. Last check: 2007-10-02)
		be a faithful unitary representation whose matrix coefficient functions vanish at infinity and satisfy an appropriate integrabillty condition.
		We apply this result to a symplectic group and the Weil representation associated to a quadratic form.
		As the tensor products of such a representation are also Weil representations (associated to different forms), we see that any discrete series representation can be realized as a subrepresentation of a Weil representation.
	www.hindawi.com /journals/ijmms/volume-1/S0161171278000277.html (143 words)

	MATH 630 (Site not responding. Last check: 2007-10-02)
		W 1/28 - I gave examples of matrix groups and finite-dimensional representations of them.
		F 1/30 - I talked about unitary representations, invariant subspaces, and complete reducibility of finite-dimensional unitary representations.
		Monday HW 6 is due and I will start lectures on infinite-dimensional unitary representations and harmonic analysis.
	www.math.umd.edu /~rah/m636syl.html (817 words)

	some bibliography: K
		representation theory of affine Lie superalgebras is quite different from that of affine Lie algebras...
		For three particular values of the parameter, the theorem specializes to known results: the Thoma theorem describing characters of the infinite symmetric group, the Kingman classification of partition structures, and the description of spherical functions of the infinite hyperoctahedral Gelfand pair.
		Representations of sl(2) and rank 2 simple Lie algebras are spidertized.
	www.justpasha.org /math/bib/k.html (6561 words)

	Zelevinsky: Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm ... (Site not responding. Last check: 2007-10-02)
		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.
		CASSELMAN, Introduction to the Theory of Admissible Representations of p-Adic Reductive Groups, preprint.
	www-mathdoc.ujf-grenoble.fr /numdam-bin/item?id=ASENS_1980_4_13_2_165_0 (208 words)

	Representation Theory
		Abstract: We study the problem of constructing a contragredient functor on the category of admissible locally analytic representations of
		Borel A., Wallach N., Continuous cohomology, Discrete Subgroups, and Representations of Reductive Groups, Ann.
		Casselman W., Introduction to the theory of admissible representations of
	www.ams.org /ert/2005-009-10/S1088-4165-05-00277-3/home.html (306 words)

	Gelbart, Jacquet: A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
		Gelbart, Jacquet: A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
		A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$.
		GELBART, Weil's Representation and the Spectrum of the Metaplectic Group (Springer Lecture Notes, Vol.
	www-mathdoc.ujf-grenoble.fr /numdam-bin/item?id=ASENS_1978_4_11_4_471_0 (302 words)

	[No title] (Site not responding. Last check: 2007-10-02)
		COURSE SYLLABUS Course Number: MATH 7330 Course Title: Linear Representations of Finite Groups Credit Hours: 3 Prerequisites: MATH 7320 Corequisite: Objectives: To introduce students to the theory of representations of finite groups and its application to the determination of group structure.
		To reinforce and expand on students' understanding of basic notions in algebra, such as groups, rings, vector spaces, modules, categories.
		In order to successfully complete the course the student will have to demonstrate an ability to creatively examine and apply the mathematics presented in the course.
	www.auburn.edu /~smith01/txtsyll/syl7330.txt (431 words)

	IRMA Strasbourg - Publication 2000 (Site not responding. Last check: 2007-10-02)
		Carayol, who attributes the conjecture in part to Drinfeld, predicts in \cite{Carayol} that this representation $\Psi_d$ <> both the local Langlands correspondence (between representations of $\gl_d(K)$ and $W_K$) and the local Jacquet-Langlands correspondence (between representations of $\gl_d(K)$ and $D_d^*$).
		Precisely, we show in this article that the isotypic component $\Psi_d(\pi)$, for $\pi$ a supercuspidal representation of $\gl_d(K)$, is isomorphic to the tensor product $\mbox{JL}(\pi^\vee)\otimes\widetilde{\sigma}_d(\pi^\vee)$, where $\mbox{JL}(\pi^\vee)$ (resp.
		$\widetilde{\sigma}_d(\pi^\vee)$) denotes the representation corresponding to the contragredient $\pi^\vee$ of $\pi$ under the local Jacquet-Langlands correspondence (resp.
	www-irma.u-strasbg.fr /irma/publications/2000/00039.shtml (232 words)

	Bernstein, Zelevinsky: Induced representations of reductive ${\germ p}$-adic groups. I
		Bernstein, I. Zelevinsky, A. Induced representations of reductive ${\germ p}$-adic groups.
		ZELEVINSKY, Induced Representations of the Group GL (n) over a p-adic Field (Funkt.
		KAJDAN, On Representations of the Group GL (n, K), where K is a local Field (Funkt.
	www.numdam.org /numdam-bin/recherche?h=nc&id=ASENS_1977_4_10_4_441_0 (190 words)

	Algebra Seminar Listings
		Title: Representation of quadratic forms by sum of squares
		Title: Distinguishing contragredient Galois representations in characteristic 2
		Title: Extensions of representations of integral quadratic forms
	www.wesleyan.edu /math/Seminars/algebra.htt (263 words)

	Coherent States from Nonunitary Representations (Site not responding. Last check: 2007-10-02)
		We try to obtain a transformation of wavelet-type with a reproducing property on the unit circle using the group of Möbius transformations.
		Since the natural unitary representations of this group are not square integrable, we use a nonunitary representation together with its contragredient representation.
		We also present conditions under which this approach works in general.
	www.uni-hohenheim.de /~gzim/Publications/habil.html (74 words)

	Citebase - Differential Calculus on Quantum Spheres (Site not responding. Last check: 2007-10-02)
		On the Construction of Covariant Differential Calculi on Quantum Homogeneous Spaces [ Abstract/Citations, Cached PDF ]
		Let A be a coquasitriangular Hopf algebra and X the subalgebra of A generated by a row of a matrix corepresentation u or by a row of u and a row of the contragredient representation u
		In the paper left-covariant first order differential calculi on the quantum group A are constructed and the corr
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/9802087 (1026 words)

	[No title]
		## ## 'MatGroupSagGroup' returns a matrix group that gives the representation ## of the group
		Length(gens)]}, true); NM := N mod M; field := GF (G.weights[ first ][ 3 ]); matgens := [ ]; # take all necessary generators of G and calculate matrix representation for i in [ 1..
		dual representation ## ## 'ModuleDescrSagGroup' returns a matrix group that gives the dual ## representation of the group
	wwwcsif.cs.ucdavis.edu /~farrens/academic/250A/benchmarks/SPEC2K/cdrom/benchspec/CINT2000/254.gap/data/all/input/sagsbgrp.g (1396 words)

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