Combinatorial Gelfand models for some semigroups and q-rook monoid algebras
نویسندگان
چکیده
منابع مشابه
Combinatorial 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...
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The q-rook monoid Rn(q) is a semisimple C(q)-algebra that specializes when q → 1 to C[Rn], where Rn is the monoid of n × n matrices with entries from {0, 1} and at most one nonzero entry in each row and column. We use a Schur-Weyl duality between Rn(q) and the quantum general linear group Uqgl(r ) to compute a Frobenius formula, in the ring of symmetric functions, for the irreducible characters...
متن کاملRepresentation theory of q-rook monoid algebras
We show that, over an arbitrary field, q-rook monoid algebras are iterated inflations of Iwahori-Hecke algebras, and, in particular, are cellular. Furthermore we give an algebra decomposition which shows a q-rook monoid algebra is Morita equivalent to a direct sum of Iwahori-Hecke algebras. We state some of the consequences for the representation theory of q-rook monoid algebras.
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When we were at the beginnings of our careers Sergei’s support helped us to believe in our work. He generously encouraged us to publish our results on Brauer and Birman-Murakami-Wenzl algebras, results which had in part, or possibly in total, been obtained earlier by Sergei himself. He remains a great inspiration for us, both mathematically and in our memory of his kindness, modesty, generosity...
متن کاملCombinatorial Gelfand Models for Semisimple Diagram Algebras
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.
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2009
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091507001216