Affine crystals, one-dimensional sums and parabolic Lusztig q-analogues

Details Affine crystals, one-dimensional sums and parabolic Lusztig q-analogues Affine crystals, one-dimensional sums and parabolic Lusztig q-analogues

2010-02-19

arxiv.org/abs/1002.3715v2

Mathematics

Quantum Algebra

37 pages; proof of Theorem 8.1 simplified; revised in several places and typos corrected

Scientific paper

This paper is concerned with one-dimensional sums in classical affine types. We prove a conjecture of the third author and Zabrocki by showing they all decompose in terms of one-dimensional sums related to affine type A provided the rank of the root system considered is sufficiently large. As a consequence, any one-dimensional sum associated to a classical affine root system with sufficiently large rank can be regarded as a parabolic Lusztig q-analogue.

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