Crystal Bases for the Quantum Superalgebra U_q(gl(m,n))

1998/10/15 by Georgia Benkart, Seok-Jin Kang, Benkart, Georgia +3 · 2 citations
Mathematics · #17B37 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/9810092

55 pages, many figures drawn with "texdraw"

arxiv created 1998/10/15 · arxiv updated 2009/11/30

Abstract

We develop a crystal base theory for the general linear Lie superalgebra gl(m,n). We prove that any irreducible U_q(gl(m,n))-module in some category has a crystal base, and prove that its associated crystal base is parameterized by semistandard tableaux.

Cited by

• Character Formulas for Kirillov-Reshetikhin Modules via Folding of Supercharacters of \mathfrakgl(M|N)
• q-deformed Howe duality for orthosymplectic Lie superalgebras

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