Gelfand criterion and multiplicity one results for $$\mathrm {GL}_n$$ GL n over finite chain rings

Shiv Prakash Patel () and Pooja Singla ()
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Shiv Prakash Patel: Indian Institute of Technology Delhi
Pooja Singla: Indian Institute of Technology Kanpur

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 3, 761-772

Abstract: Abstract We study the Whittaker space of $$\mathrm {GL}_n(\mathcal {O}/(\varpi ^\ell ))$$ GL n ( O / ( ϖ ℓ ) ) where $$\ell \ge 1$$ ℓ ≥ 1 , $$\mathcal {O}$$ O is the ring of integers of a non-Archimedean local field and $$\varpi $$ ϖ is a uniformizer of $$\mathcal {O}$$ O . By using Gelfand criterion, we prove that the Whittaker space is multiplicity free for $$n = 2,3$$ n = 2 , 3 . We also state a few related open questions.

Keywords: Whittaker space; Multiplicity one; Gelfand–Graev model; Gelfand criterion; Primary 20G05; Secondary 20G25 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00188-4

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