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THE ANNIHILATOR OF TENSOR SPACE IN THE $q$-ROOK MONOID ALGEBRA

Part of: Semigroups Algebraic combinatorics Linear algebraic groups and related topics Representation theory of groups

Published online by Cambridge University Press:  02 March 2017

ZHANKUI XIAO
ZHANKUI XIAO*
Affiliation:
School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, 362021, P. R. China email [email protected]
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Abstract

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In this paper, we give an explicit construction of a quasi-idempotent in the $q$-rook monoid algebra $R_{n}(q)$ and show that it generates the whole annihilator of the tensor space $U^{\otimes n}$ in $R_{n}(q)$.

Keywords

tensor spaceq-rook monoidSchur–Weyl duality

MSC classification

Primary: 20C08: Hecke algebras and their representations
Secondary: 05E10: Combinatorial aspects of representation theory 20G05: Representation theory 20M30: Representation of semigroups; actions of semigroups on sets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 1 , August 2017 , pp. 77 - 86
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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