Formulas for coefficients in the based ring of the lowest two-sided cell are derived in terms of generalized exponents, and a seemingly new positive basis is defined for the subring.
Dawydiak, On Lusztig’s asymptotic Hecke algebra for SL2, Proc
2 Pith papers cite this work. Polarity classification is still indexing.
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J(G) for inner forms G of p-adic GL_n is defined over ar Q_l, admits explicit formulas via reductive centralizers, shares Hochschild homology with C_c^infty(G), and supports rudimentary Hecke compatibility for sheaves on Bun_n.
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A positivity property in the based ring of the lowest two-sided cell
Formulas for coefficients in the based ring of the lowest two-sided cell are derived in terms of generalized exponents, and a seemingly new positive basis is defined for the subring.
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On Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of $\mathrm{GL}_n$
J(G) for inner forms G of p-adic GL_n is defined over ar Q_l, admits explicit formulas via reductive centralizers, shares Hochschild homology with C_c^infty(G), and supports rudimentary Hecke compatibility for sheaves on Bun_n.