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Hecke algebras, Specht modules and Grobner-Shirshov bases
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kang, Seok-Jin | - |
dc.contributor.author | Lee, In-Sok | - |
dc.contributor.author | Lee, Kyu-Hwan | - |
dc.contributor.author | Oh, Hyekyung | - |
dc.date.accessioned | 2009-11-15T22:50:51Z | - |
dc.date.available | 2009-11-15T22:50:51Z | - |
dc.date.issued | 2002 | - |
dc.identifier.citation | J. Algebra 252 (2002) 258-292 | en |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.uri | https://hdl.handle.net/10371/12148 | - |
dc.description.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. | en |
dc.description.sponsorship | 1. This research was supported by KOSEF Grant # 98-0701-01-5-L and BK21 Mathematical
Sciences Division, Seoul National University. 2. This research was supported in part by the Young Scientist Award, Korean Academy of Science and Technology. | en |
dc.language.iso | en | - |
dc.publisher | Elsevier | en |
dc.subject | Specht modules | en |
dc.subject | Hecke algebras | en |
dc.subject | Gröbner–Shirshov basis | en |
dc.subject | monomial basis | en |
dc.title | Hecke algebras, Specht modules and Grobner-Shirshov bases | en |
dc.type | Article | en |
dc.contributor.AlternativeAuthor | 강석진 | - |
dc.contributor.AlternativeAuthor | 이인석 | - |
dc.contributor.AlternativeAuthor | 이규환 | - |
dc.contributor.AlternativeAuthor | 오혜경 | - |
dc.identifier.doi | 10.1016/S0021-8693(02)00071-6 | - |
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