Matrix Units for Centralizer Algebras
نویسندگان
چکیده
We compute matrix units for Brauer’s centralizer algebras and Hecke algebras of type A. This can be used to construct a complete system of matrix units of the centralizers of tensor products of classical Lie groups (except S0(2n)) and their quantum deformations. The calculation is done by induction inspired by path models for special operator algebras. It is similar to the calculation of Young’s orthogonal matrix units for the symmetric group as given by Rutherford.
منابع مشابه
Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. I. Permutation Groups and Coherent (cellular) Algebras
Let (G;) be a permutation group of degree n. Let V (G;) be the set of all square matrices of order n which commute with all permutation matrices corresponding to permutations from (G;): V (G;) is a matrix algebra which is called the centralizer algebra of (G;): In this paper we introduce the combinatorial analogue of centralizer algebras, namely coherent (cellular) algebras and consider the pro...
متن کاملCharacters of Brauer's Centralizer Algebras
Brauer's centralizer algebras are finite dimensional algebras with a distinguished basis. Each Brauer centralizer algebra contains the group algebra of a symmetric group as a subalgebra and the distinguished basis of the Brauer algebra contains the permutations as a subset. In view of this containment it is desirable to generalize as many known facts concerning the group algebra of the symmetri...
متن کاملDegenerate two-boundary centralizer algebras
Diagram algebras (e.g. graded braid groups, Hecke algebras, Brauer algebras) arise as tensor power centralizer algebras, algebras of commuting operators for a Lie algebra action on a tensor space. This work explores centralizers of the action of a complex reductive Lie algebra g on tensor space of the form M ⊗ N ⊗ V ⊗k. We define the degenerate two-boundary braid group Gk and show that centrali...
متن کاملCentralizer Construction for Twisted Yangians
For each of the classical Lie algebras g(n) = o(2n+ 1), sp(2n), o(2n) of type B, C, D we consider the centralizer of the subalgebra g(n−m) in the universal enveloping algebra U(g(n)). We show that the nth centralizer algebra can be naturally projected onto the (n− 1)th one, so that one can form the projective limit of the centralizer algebras as n → ∞ with m fixed. The main result of the paper ...
متن کاملComputing the Discriminants of Brauer's Centralizer Algebras
This paper discusses a computational problem arising in the study of the structure theory of Brauer's orthogonal and symplectic centralizer algebras. The problem is to compute the ranks of certain combinatorially defined matrices Zm k(x) (these matrices are presented in §2). This computation is difficult because the sizes of the matrices Zm k(x) are enormous even for small values of m and k . H...
متن کامل