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arXiv · 2407.06865

Affine $\imath$quantum groups and Steinberg varieties of type C

Changjian Su·Weiqiang Wang
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Abstract

We provide a geometric realization of the quasi-split affine $\imath$quantum group of type AIII$_{2n-1}^{(\tau)}$ in terms of equivariant K-groups of non-connected Steinberg varieties of type C. This uses a new Drinfeld type presentation of this affine $\imath$quantum group which admits very nontrivial Serre relations. We then construct \`a la Springer a family of finite-dimensional standard modules and irreducible modules of this $\imath$quantum group, and provide a composition multiplicity formula of the standard modules.

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Changjian Su, Weiqiang Wang. 2024-07-09. Affine $\imath$quantum groups and Steinberg varieties of type C. https://doi.org/10.1007/s00029-026-01161-x

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