Combinatorial Gelfand Models for Semisimple Diagram Algebras
نویسنده
چکیده
We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebras, their partial analogues, walled Brauer algebras, their partial analogues, Temperley-Lieb algebras, their partial analogues, walled Temperley-Lieb algebras, their partial analogues, partition algebras and their Temperley-Lieb analogues.
منابع مشابه
Gelfand Models for Diagram Algebras : extended abstract
A Gelfand model for a semisimple algebra A over C is a complex linear representation that contains each irreducible representation of A with multiplicity exactly one. We give a method of constructing these models that works uniformly for a large class of combinatorial diagram algebras including: the partition, Brauer, rook monoid, rook-Brauer, Temperley-Lieb, Motzkin, and planar rook monoid alg...
متن کاملSolitary Bases for Irreducible Representations of Semisimple Lie Algebras∗
The main results of this paper were found while addressing the question: what do the “nice” bases for the irreducible representations of semisimple Lie algebras look like? Using the Gelfand-Zetlin bases for the irreducible representations of gl(n,C) as our model, we take a combinatorial approach to this question by associating a certain kind of directed graph to each weight basis for an irreduc...
متن کاملCombinatorial Constructions of Weight Bases: The Gelfand-Tsetlin Basis
This work is part of a project on weight bases for the irreducible representations of semisimple Lie algebras with respect to which the representation matrices of the Chevalley generators are given by explicit formulas. In the case of sln, the celebrated Gelfand-Tsetlin basis is the only such basis known. Using the setup of supporting graphs developed by Donnelly, we present a new interpretatio...
متن کاملCombinatorial Gelfand models for some semigroups and q-rook monoid algebras
Inspired by the results of [APR], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebr...
متن کاملLecture 5: Semisimple Lie Algebras over C
In this lecture I will explain the classification of finite dimensional semisimple Lie algebras over C. Semisimple Lie algebras are defined similarly to semisimple finite dimensional associative algebras but are far more interesting and rich. The classification reduces to that of simple Lie algebras (i.e., Lie algebras with non-zero bracket and no proper ideals). The classification (initially d...
متن کامل