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Character formulae for queer Lie superalgebras and canonical bases of types \(A/C\). (English) Zbl 1406.17014
Summary: 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.

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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