منابع مشابه
Character Formulas for q-Rook Monoid Algebras
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.
متن کاملq-rook monoid algebras, Hecke algebras, and Schur-Weyl duality
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 کاملRepresentations of the rook monoid
Let n be a positive integer and let n = {1, . . . , n}. Let R be the set of all oneto-one maps σ with domain I (σ ) ⊆ n and range J (σ) ⊆ n. If i ∈ I (σ ) let iσ denote the image of i under σ . There is an associative product (σ, τ ) → στ on R defined by composition of maps: i(στ)= (iσ )τ if i ∈ I (σ ) and iσ ∈ I (τ ). Thus the domain I (στ) consists of all i ∈ I (σ ) such that iσ ∈ I (τ ). The...
متن کاملFast Fourier Transforms for the Rook Monoid
We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divideand-conquer algorithms (fast Fourier transforms, or FFTs) for computing it. This paper marks the first extension of group FFTs to non-group semigroups.
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ژورنال
عنوان ژورنال: Acta Mathematica Sinica, English Series
سال: 2016
ISSN: 1439-8516,1439-7617
DOI: 10.1007/s10114-016-5546-8