Affine $ı$quantum groups and Steinberg varieties of type C

Abstract

We provide a geometric realization of the quasi-split affine $ı$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 $ı$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 $ı$quantum group, and provide a composition multiplicity formula of the standard modules.

Final version, corrected some errors in v2 and in literature

References in corpus (5)

• Braid Group Action and Quantum Affine Algebras
• A Drinfeld type presentation of affine $ı$quantum groups II: split BCFG type
• Braid group action and quasi-split affine $ı$quantum groups I
• Affine $ı$quantum groups and twisted Yangians in Drinfeld presentations
• A Drinfeld type presentation of twisted Yangians of quasi-split type