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arXiv · 2209.12378

Local coefficients and Gelfand-Graev representations for non-split covers on SL(2)

Yeongseong Jo
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Abstract

A purely local approach has been developed by Krishnamurthy and Kutzko to compute Langlands-Shahidi local coefficient for ${\rm SL}(2)$ via types and covers \`{a} la Bushnell-Kutzko. In this paper, we extend their method to the non-split case and complete their project. We also study the algebraic structure of Gelfand-Graev representations, which generalizes the results of Chan-Savin and Mishra-Pattanayak to ${\rm SL}(2)$ over non-archimidean local fields without any restriction on the characteristic.

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Yeongseong Jo. 2022-09-26. Local coefficients and Gelfand-Graev representations for non-split covers on SL(2). https://arxiv.org/abs/2209.12378

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