Abstract
This paper is concerned with one-dimensional sums in classical affine types. We prove a conjecture of Shimozono and Zabrocki (J Algebra 299:33–61, 2006) 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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Lecouvey, C., Okado, M. & Shimozono, M. Affine crystals, one-dimensional sums and parabolic Lusztig q-analogues. Math. Z. 271, 819–865 (2012). https://doi.org/10.1007/s00209-011-0892-9
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DOI: https://doi.org/10.1007/s00209-011-0892-9