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arXiv · 1804.03710

The Steinberg-Lusztig tensor product theorem, Casselman-Shalika and LLT polynomials

Martina Lanini·Arun Ram
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Abstract

In this paper we establish a Steinberg-Lusztig tensor product theorem for abstract Fock space. This is a generalization of the type A result of Leclerc-Thibon and a Grothendieck group version of the Steinberg-Lusztig tensor product theorem for representations of quantum groups at roots of unity. Although the statement can be phrased in terms of parabolic affine Kazhdan-Lusztig polynomials and thus has geometric content, our proof is combinatorial, using the theory of crystals (Littelmann paths). We derive the Casselman-Shalika formula as a consequence of the Steinberg-Lusztig tensor product theorem for abstract Fock space.

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Martina Lanini, Arun Ram. 2018-04-10. The Steinberg-Lusztig tensor product theorem, Casselman-Shalika and LLT polynomials. https://arxiv.org/abs/1804.03710

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