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Fourier Transform and the minimal representation of
Wee Teck Gan, Nadya Gurevich
We consider the minimal representation of the adjoint split group over a p-adic field. The representation has a model in a space of functions on a 17 dimensional cone , an…
Automorphic functionals for the minimal representations of groups of type and
Nadya Gurevich, David Kazhdan
Let be a split simply-connected group of type or . The minimal automorphic representation of admits a realization on a space of functions $\mathcal S(…
Fourier transform on a cone and the minimal representation of even orthogonal group
Nadya Gurevich, David Kazhdan
Let be an even orthogonal quasi-split group defined over a local non-archimedean field . We describe the subspace of smooth vectors of the minimal representation of …
Genuine pro- Iwahori--Hecke algebras, Gelfand--Graev representations, and some applications
Fan Gao, Nadya Gurevich, Edmund Karasiewicz
We study the Iwahori-component of the Gelfand-Graev representation of a central cover of a split linear reductive group and utilize our results for three applications. In fact, it…
The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups
Nadya Gurevich, Edmund Karasiewicz
We prove the Casselman-Shalika formula for unramified groups over a non-archimedean local field by studying the action of the spherical Hecke algebra on the space of compact spheri…
Fourier transforms on the basic affine space of a quasi-split group
Nadya Gurevich, David Kazhdan
We extend the Gelfand and Graev construction of generalized Fourier transforms on basic affine space from split groups to quasi-split groups over a local non-archimedean field .
Poles of the Standard -function of and the Rallis-Schiffmann Lift
Nadya Gurevich, Avner Segal
We characterize the cuspidal representations of whose standard -function admits a pole at as the image of Rallis-Schiffmann lift for the commuting pair $\l…
The twisted Satake isomorphism and Casselman-Shalika formula
Nadya Gurevich
For an arbitrary split adjoint group we identify the unramified Whittaker space with the space of skew-invariant functions on the lattice of coweights and deduce from it the Cassel…
Rankin-Selberg integral with Non-unique model for the standard L-function of
Nadya Gurevich, Avner Segal
Let L^S(π,s,st) be a partial L-function of degree 7 of a cuspidal automorphic representation πof the exceptional group G_2. Here we construct a Rankin-Selberg integral for represen…