2015/04/15 by Kentaro Wada, Wada, Kentaro
Mathematics · Physics and Astronomy · #17B10 #17B37 #20G43 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1504.03863
openalex publication_date 2015/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a Lie algebra \mathfrakgQ(m) and an associative algebra Uq,Q(m) associated with the Cartan data of \mathfrakglm which is separated into r parts with respect to m=(m1, …, mr) such that m1+ … + mr =m. We show that the Lie algebra \mathfrakgQ (m) is a filtered deformation of the current Lie algebra of \mathfrakglm, and we can regard the algebra Uq, Q(m) as a "q-analogue" of U(\mathfrakgQ(m)). Then, we realize a cyclotomic q-Schur algebra as a quotient algebra of Uq, Q(m) under a certain mild condition. We also study the representation theory for \mathfrakgQ(m) and Uq,Q(m), and we apply them to the representations of the cyclotomic q-Schur algebras.