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

Changjian Su; Weiqiang Wang

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

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arxiv 2407.06865 v4 pith:TOFEXM3Y submitted 2024-07-09 math.RT math.QA

Changjian Su , Weiqiang Wang This is my paper · ORCID

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keywords imathquantumtypeaffinegroupmodulesstandardsteinberg

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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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Geometric construction of Schur algebras
math.RT 2024-11 conditional novelty 6.0 of 10

For any finite type, generalized Schur algebras are realized as convolution algebras in Borel-Moore homology and equivariant K-theory of Steinberg varieties.

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