Seminar in Representation Theory
Quantum wreath products and pro-p metaplectic Hecke algebras
2026/03/02 (Mon.) 14:00~16:00
- Date : 2026/03/02 (Mon.) 14:00~16:00
- Location : Seminar Room 617, Institute of Mathematics (NTU Campus)
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Speaker : Chun-Ju Lai (Institute of Mathematics, Academia Sinica)
- Abstract :
We develop the theory of quantum wreath products of skew polynomial type and use it to provide transparent descriptions of the pro-p Iwahori–Hecke algebra and its Gelfand–Graev modules for the p-adic general linear group and its metaplectic covers, which were previously inaccessible through standard p-adic methods. Our realization uses the notion of antispherical and Kashiwara–Miwa–Stern modules for these quantum wreath products, introduced for the first time.
As an application, we give algebraic (re)proofs of several results of p-adic interest including (1) the existence of PBW basis for the pro-p metaplectic and Iwahori–Hecke algebras, (2) identification of the Iwahori–Schur algebra with the quantum affine Schur algebra, (3) the failure of the local Shimura correspondence at the pro-p level, and (4) the failure of the multiplicity one property for the metaplectic group. This is a joint work with Valentin Buciumas.
