Character formulae for queer Lie superalgebras and canonical bases of types $A/C$

Abstract

For the BGG category of $\mathfrak{q}(n)$-modules of half-integer weights, a Kazhdan-Lusztig conjecture à la Brundan is formulated in terms of categorical canonical basis of the $n$th tensor power of the natural representation of the quantum group of type $C$. For the BGG category of $\mathfrak{q}(n)$-modules of congruent non-integral weights, a Kazhdan-Lusztig conjecture is formulated in terms of canonical basis of a mixed tensor of the natural representation and its dual of the quantum group of type $A$. We also establish a character formula for the finite-dimensional irreducible $\mathfrak{q}(n)$-modules of half-integer weights in terms of type $C$ canonical basis of the corresponding $q$-wedge space.

32 pages, minor revision on v2, to appear in Communications in Mathematical Physics

References in corpus (2)

• Regular strongly typical blocks of ${\mathcal{O}}^{\mathfrak{q}}$
• Finite-dimensional half-integer weight modules over queer Lie superalgebras

Cited by in corpus (3)

• A basis theorem for the degenerate affine oriented Brauer-Clifford supercategory
• Supercharacters of queer Lie superalgebras
• Candidate for the crystal $B(-\infty )$ for the queer Lie superalgebra