q-Deformed Fock spaces and modular representations of spin symmetric groups

Abstract

We use the Fock space representation of the quantum affine algebra of type $A_{2n}^{(2)}$ to obtain a description of the global crystal basis of its basic level 1 module. We formulate a conjecture relating this basis to decomposition matrices of spin symmetric groups in characteristic $2n+1$.

18 pages, Latex, epsf and iop macros (ioplppt.sty). Revised version, to appear in J. Phys. A. Some typos corrected, and some comments added in the introduction

References in corpus (3)

• Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies
• A proof of polynomial identities of type $\widehat{sl(n{)}_1}\otimes \widehat{sl(n{)}_1}/\widehat{sl(n{)}_2}$
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Cited by in corpus (11)

• Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)
• Dual canonical bases, quantum shuffles and q-characters
• Decomposition numbers for abelian defect RoCK blocks of double covers of symmetric groups
• Schur partition theorems via perfect crystal
• Crossover Morita equivalences of spin representations of the symmetric and alternating groups
• Modular branching rules for projective representations of symmetric groups and lowering operators for the supergroup Q(n)
• Mullineux involution and twisted affine Lie algebras
• Yang-Baxter bases of 0-Hecke algebras and representation theory of 0-Ariki-Koike-Shoji algebras
• Hecke-Clifford superalgebras, crystals of type A_{2l}^{(2)} and modular branching rules for \hat S_n
• sl_2-actions along short strings for spin blocks
• Young walls and graded dimension formulas for finite quiver Hecke algebras of type $A_{2\ell }^{(2)}$ and $D_{\ell +1}^{(2)}$