Affine $\imath$quantum groups and Steinberg varieties of type C
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 à 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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.06865
- arXiv:
- arXiv:2407.06865
- Bibcode:
- 2024arXiv240706865S
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Quantum Algebra
- E-Print:
- References updated