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<p>Let <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathfrak {g}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">g</mi> </math></EquationSource> </InlineEquation> be a complex semisimple Lie algebra and let <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textbf{U}_q(\mathfrak g)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold">U</mi> <mi>q</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> denote the associated Drinfel’d Jimbo quantized enveloping algebra. In this paper we study spherical functions of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\textbf{U}_q(\mathfrak g)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold">U</mi> <mi>q</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> related to characters. We show invariance under the Wang-Zhang braid group operators and show relative Weyl group invariance, when restricted to the quantum torus.</p>

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Symmetries for Spherical Functions of Type \(\chi \) for Quantum Symmetric Pairs

  • 期刊论文

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  • 发表日期：

    2025年3月22日

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  • Stein Meereboer

摘要

Let \(\mathfrak {g}\) g be a complex semisimple Lie algebra and let \(\textbf{U}_q(\mathfrak g)\) U q ( g ) denote the associated Drinfel’d Jimbo quantized enveloping algebra. In this paper we study spherical functions of \(\textbf{U}_q(\mathfrak g)\) U q ( g ) related to characters. We show invariance under the Wang-Zhang braid group operators and show relative Weyl group invariance, when restricted to the quantum torus.