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<p>We introduce the space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\cal{MV}_{n|m}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mi mathvariant="script">M</mi> <mi mathvariant="script">V</mi> </mrow> <mrow> <mi mathvariant="script">n</mi> <mrow> <mo class="MJX-tex-caligraphic" mathvariant="script" stretchy="false">|</mo> </mrow> <mi mathvariant="script">m</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> as the space of <i>G</i>-invariant functions on the variety of triples of two partial flag varieties and a vector space. Subsequently, we define the action of the mirabolic quantum Schur algebra via convolution multiplication. Finally, we present the geometric approach of the mirabolic Howe duality.</p>

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Mirabolic Howe Duality

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Zhaobing Fan,
  • Haitao Ma,
  • Zhicheng Zhang

摘要

We introduce the space \(\cal{MV}_{n|m}\) M V n | m as the space of G-invariant functions on the variety of triples of two partial flag varieties and a vector space. Subsequently, we define the action of the mirabolic quantum Schur algebra via convolution multiplication. Finally, we present the geometric approach of the mirabolic Howe duality.