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<p>We provide a geometric realization of the quasi-split affine iquantum group of type <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\text {AIII}_{2n-1}^{(\tau )}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mtext>AIII</mtext> <mrow> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation> in terms of equivariant K-groups of non-connected Steinberg varieties of type C. This uses a new Drinfeld type presentation of this affine iquantum 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 iquantum group, and provide a composition multiplicity formula of the standard modules.</p>

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Affine \(\text {i}\)quantum groups and Steinberg varieties of type C

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Changjian Su,
  • Weiqiang Wang

摘要

We provide a geometric realization of the quasi-split affine iquantum group of type \(\text {AIII}_{2n-1}^{(\tau )}\) AIII 2 n - 1 ( τ ) in terms of equivariant K-groups of non-connected Steinberg varieties of type C. This uses a new Drinfeld type presentation of this affine iquantum 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 iquantum group, and provide a composition multiplicity formula of the standard modules.