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Hecke algebras, Specht modules and Grobner-Shirshov bases

Cited 18 time in Web of Science Cited 21 time in Scopus
Authors
Kang, Seok-Jin; Lee, In-Sok; Lee, Kyu-Hwan; Oh, Hyekyung
Issue Date
2002
Publisher
Elsevier
Citation
J. Algebra 252 (2002) 258-292
Keywords
Specht modulesHecke algebrasGröbner–Shirshov basismonomial basis
Abstract
In this paper, we study the structure of Specht modules over Hecke algebras using
the Gröbner–Shirshov basis theory for the representations of associative algebras. The
Gröbner–Shirshov basis theory enables us to construct Specht modules in terms of
generators and relations. Given a Specht module S^λ_q, we determine the Gröbner–Shirshov pair (Rq ,R^λ_q) and the monomial basis G(λ) consisting of standard monomials. We show that the monomials in G(λ) can be parameterized by the cozy tableaux. Using the division algorithm together with the monomial basis G(λ), we obtain a recursive algorithm of computing the Gram matrices. We discuss its applications to several interesting examples including Temperley–Lieb algebras.
ISSN
0021-8693
Language
English
URI
https://hdl.handle.net/10371/12148
DOI
https://doi.org/10.1016/S0021-8693(02)00071-6
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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