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The ( Q, q )‐Schur Algebra
Author(s) -
Dipper R,
James G,
Mathas A
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000483
Subject(s) - mathematics , schur algebra , hecke algebra , algebra over a field , basis (linear algebra) , cellular algebra , pure mathematics , field (mathematics) , ring (chemistry) , symmetric algebra , construct (python library) , division algebra , filtered algebra , algebra representation , orthogonal polynomials , classical orthogonal polynomials , gegenbauer polynomials , chemistry , geometry , organic chemistry , computer science , programming language
In this paper we use the Hecke algebra of type B to define a new algebra S which is an analogue of the q ‐Schur algebra. We show that S has ‘generic’ basis which is independent of the choice of ring and the parameters q and Q . We then construct Weyl modules for S and obtain, as factor modules, a family of irreducible S‐modules defined over any field. 1991 Mathematics Subject Classification : 16G99, 20C20, 20G05.