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<p>In this paper, we study the mirabolically induced modules for the loop and affine algebras of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathfrak {sl}_m\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="fraktur">sl</mi> <mi>m</mi> </msub> </math></EquationSource> </InlineEquation>. Among the main results, we give a free field realization of all irreducible mirabolically induced modules, and obtain a character formula for such modules with finite dimensional weight spaces.</p>

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Mirabolically Induced Modules for Loop and Affine \({\mathfrak {sl}}_{m}\)

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Fulin Chen,
  • Zhiqiang Li,
  • Shaobin Tan

摘要

In this paper, we study the mirabolically induced modules for the loop and affine algebras of \(\mathfrak {sl}_m\) sl m . Among the main results, we give a free field realization of all irreducible mirabolically induced modules, and obtain a character formula for such modules with finite dimensional weight spaces.