J-P. Serre. Linear Representations of Finite Groups. Springer-Verlag, New York, 1977. Home/Search Document Not in Database Summary Related Articles Check |
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The Covariance Structure of Random Permutation Matrices - Viana (Correct)
....complex solutions, if all eigenvalues of M or are zero then the proposition holds. Otherwise, let # be a non zero eigenvalue of M, # a non zero eigenvalue of M, K = kern M #I and = kern M #I . We will show that both K and are subspaces of W stable under G, and use the fact[e.g. Ser77, p.17] Dia88, p.6] and Appendix A] that V and W are irreducible subspaces of the linear representation #. Consequently, both K and must reduce to null subspaces, and this will complete the proof. 1) K W . First note that e # M = e # ( 0, so that for v K we have (M #I)v =0=e ....
....defined by #) T = 2 1 . From (5.3) we obtain E(cn (U)c # n (U) T# # #T # = T 600 020 003 T # = 2 1 which is as derived in Example 5.1. Appendix A. The (n 1) dimensional irreducible representation of G. The existence and construction of the representation is outlined in [Ser77, p.17] and also in [Dia88, pp.6,134] Let # indicate the permutation representation on the symmetric group (G) acting on a set X with n objects and let Y indicate the product of p copies of X, p =1, n. Let al.so # indicate the character of #. 1) The character of # acting on Y is # ; 2) ....
Jean-Pierre Serre, Linear representations of finite groups, Springer-Verlag, New York, 1977.
Decomposing Permutation Representations of Symmetric Groups - Wildon (2001) (Correct)
.... Let K be a field of characteristic 0, su# ciently large so that every irreducible representation of G defined over K is absolutely irreducible; i.e. if V is an irreducible representation of G over K, then V remains irreducible even if we extend K to some larger field) It can be shown (see Serre [12] 12.3) that if N is the lowest common multiple of the orders of elements of G, then a su#cient condition is that K contains a primitive N root of unity. be the ring of algebraic integers in K. Choose a maximal ideal containing (p) the ideal generated by p. As M is a field of ....
....V be a KG module. Choose an L inside V . Define [V ]d = L ML = L# k] Then d : G 0 (KG) G 0 (kG) is a well defined homomorphism of abelian groups. To prove that d is well defined one must show that [V ]d is independent of the choice of maximal ideal and the choice of L. See Serre [12] 15.2 for a short proof of the latter. The need to prove the former can also be sidestepped in various ways see the remarks at the end of 1.1.1) Our examples show that if p = 2 then [QC 2 ]d = 2[F 2 ] and that if p = 3 and V is the two dimensional module defined in example 2 then [V ]d = ....
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J. P. Serre. Linear representations of finite groups. Springer GTM 42, 1977.
A Fast Program Generator of Fast Fourier Transforms - Clausen, Müller (Correct)
....called linear iff it corresponds to a representation of degree 1. By Irr(G) we denote the set of all irreducible characters of G. The space CF(G, C) of all complex valued class functions on G becomes an inner product space by xl : IGI x(a) a) for a proof of the following facts we refer to [9]: Theorem 1. For a finite group G with h conjugacy classes the following is true: 1) Irr(G) X, Xa is an orthonormal basis of CF(G, C) 2) Let F and Dk be representations of CG with characters X and Xk, respectively. f D is irreducible, then the multiplicity (D IF) with which D occurs in ....
Serre, J.P.: Linear Representations of Finite Groups. Graduate Texts in Mathematics, Springer, 1986.
Factorisations for Partition Functions of Random.. - Jackson, Perry, Visentin (1995) (Correct)
....integral The purpose of this section is to prove the factorisation theorem entirely independently of the idea of a surface. The proof is essentially an algebraic one. The reader is referred to Macdonald [25] for the details and proofs of classical results about symmetric functions, and to Serre [30]. If f is a formal power series in x; let [x ]f denote the coefficient of x in f; whenever n is a non negative integer. For n; let be the character of the ordinary irreducible representation of the symmetric group Sn ; indexed by ; and let ff denote the value of this function at ....
J-P. Serre, "Linear Representations of Finite Groups," Springer-Verlag, New York, 1977.
Plethysm, Partitions with an Even Number of Blocks and Euler.. - Sundaram (1996) (Correct)
.... of the trivial representation from the subgroup fixing the chain c 1 ; namely, the Young subgroup S 1 Theta S 3 : Hence ch(V ) h 1 h 3 : Similarly V is obtained by inducing the trivial representation from the subgroup of S 4 fixing the chain c 1 ; this is the wreath product group S 2 [S 2 ]: The operation in the ring of symmetric functions which describes representations induced from wreath product subgroups of the symmetric group is plethysm; the characteristic ch(V ) is given by the plethysm h 2 [h 2 ] of h 2 with itself. We defer the definition of plethysm until Section 4, ....
....product of the group Sm with Sn ; it consists of those permutations in Smn which permute elements within each block, or permute the blocks, or both. This wreath product subgroup can be defined more precisely as follows. Definition 3.1. The wreath product of Sm with Sn ; which we denote by Sm [S n ]; is defined to be the normaliser of the Young subgroup Sn Theta : Theta Sn in Smn : Perhaps a familiar example is the case n = 2; then Sm [S 2 ] is the hyperoctahedral group Bm of order 2 m ; which has a faithful representation as a group of m by m matrices with exactly one nonzero ....
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J.-P. Serre, Linear Representations of Finite Groups, Springer-Verlag, 1977.
Inapproximability Results for Equations over Finite Groups - Engebretsen, Holmerin.. (2004) (2 citations) (Correct)
....the 2P1R game; this is our second main technical contribution. 3 Representation theory and the Fourier transform In this section, we give a short account of the representation theory needed to state and prove our results. For more details, we refer the reader to the 5 excellent accounts by Serre [22] and Terras [25] The traditional Fourier transform, as appearing in, say, signal processing [9] algorithm design [21] or PCPs [16] focuses on decomposing functions f : G C defined over an Abelian group G. This decomposition proceeds by writing f as a linear combination of characters of ....
J.-P. Serre, Linear Representations of Finite Groups, Vol. 42 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1977.
Techniques for Deriving Extendible Linear - Parameter Spaces Ernst (2002) (Correct)
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J-P. Serre. Linear Representations of Finite Groups. Springer-Verlag, New York, 1977.
Fast Fourier Analysis for SL - Over Finite Field (Correct)
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J. P. Serre, Linear Representations of Finite Groups, Springer-Verlag, New York, 1977.
Shape Representations and Algorithms for 3D Model Retrieval - Kazhdan (2004) (Correct)
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J. Serre. Linear Representations of Finite Groups. Springer-Verlag, New York, 1977.
A Reflective Symmetry Descriptor for 3D Models - Michael Kazhdan Bernard (2003) (6 citations) (Correct)
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Serre, J.: Linear Representations of Finite Groups. Springer-Verlag, New York (1977)
Spectral Properties of Hierarchical Lattices and Iteration of.. - Sabot (Correct)
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J.P. SERRE, Linear Representations of Finite Groups, Graduated Texts in Mathematics, SpringerVerlag.
On Algebraic Singularities, Finite Graphs and D-Brane Gauge.. - He (Correct)
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J.-P. Serre, "Linear Representations of Finite Groups," Springer-Verlag, 1977.
Inapproximability Results for Equations over Finite Groups - Engebretsen, Holmerin.. (2002) (2 citations) (Correct)
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J.-P. Serre, Linear Representations of Finite Groups, Vol. 42 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1977.
Symmetry Descriptors and 3D Shape Matching - Kazhdan, Funkhouser, Rusinkiewicz (2004) (Correct)
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SERRE J.: Linear Representations of Finite Groups. Springer-Verlag, New York, 1977. 3
On Probabilistic Proof Systems and Hardness of Approximation - Holmerin (2002) (Correct)
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Jean-Pierre Serre. Linear Representations of Finite Groups, volume 42 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1977.
Inapproximability Results for Equations over Finite Groups - Engebretsen, Holmerin.. (2002) (2 citations) (Correct)
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J.-P. Serre, Linear Representations of Finite Groups, Vol. 42 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1977.
Hook Interpolations - Ron Adin Avital (Correct)
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J. P. Serre, Linear Representations of Finite Groups. Springer-Verlag, 1977.
Galois Structure of Zariski Cohomology - For Weakly Ramified (Correct)
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J.-P. Serre, "Linear representations of finite groups", Graduate Texts in Mathematics 42, Springer-Verlag, New York (1977).
Reversible Equivariant Linear Systems - Lamb, Roberts (1998) (3 citations) (Correct)
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J.-P. Serre, Linear Representations of Finite Groups, Graduate Texts in Mathematics 42, SpringerVerlag, New York, 1977.
Analysing the Quantum Fourier Transform for Finite Groups through .. - Murphy (2001) (Correct)
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J.-P. Serre. Linear Representations of Finite Groups. Graduate Texts in Mathematics, volume 42. (Springer-Verlag, New York), 1977.
Spectra of Heisenberg Graphs over Finite Rings.. - DeDeo, Martinez.. (2002) (Correct)
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J.-P. Serre, Linear Representations of Finite Groups, Springer-Verlag, N.Y., 1977.
On Evolutionary Dynamics - Christian Forst And (1996) (Correct)
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J.-P. Serre. Linear Representations of Finite Groups. Springer, 1977.
Symmetry Groups, Semidefinite Programs, and Sums of Squares - Gatermann, Parrilo (2002) (4 citations) (Correct)
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J.-P. Serre. Linear Representations of Finite Groups. Springer-Verlag, 1977.
Analysing the Quantum Fourier Transform for Finite Groups through .. - Murphy (2001) (Correct)
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J.-P. Serre. Linear Representations of Finite Groups. Graduate Texts in Mathematics, volume 42. (Springer-Verlag, New York), 1977.
The Rank of Elliptic Surfaces in Unramified Abelian Towers - Silverman (Correct)
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J.P. Serre, Linear Representations of Finite Groups, Graduate Texts in Mathematics 42, Springer-Verlag, New York, 1977
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