Wyniki wyszukiwania

1

The Cauchy Harish-Chandra Integral, for the pair $$\mathfrak{u}_{p,q} ,\mathfrak{u}_1 $$

100%

Daszkiewicz A., Przebinda T.

Open Mathematics

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2007

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tom 5

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nr 4

654-664

EN

For the dual pair considered, the Cauchy Harish-Chandra Integral, as a distribution on the Lie algebra, is the limit of the holomorphic extension of the reciprocal of the determinant. We compute that limit explicitly in terms of the Harish-Chandra orbital integrals.

2

A reverse engineering approach to the Weil representation

76%

Aubert A.-M., Przebinda T.

Open Mathematics

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2014

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tom 12

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nr 10

1500-1585

EN

We describe a new approach to the Weil representation attached to a symplectic group over a finite or a local field. We dissect the representation into small pieces, study how they work, and put them back together. This way, we obtain a reversed construction of that of T. Thomas, skipping most of the literature on which the latter is based.

3

On parabolic Whittaker functions II

64%

Oblezin S.

Open Mathematics

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2012

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tom 10

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nr 2

543-558

EN

We propose a Givental-type stationary phase integral representation for the restricted Grm,N-Whittaker function, which is expected to describe the (S 1×U N)-equivariant Gromov-Witten invariants of the Grassmann variety Grm,N. Our key tool is a generalization of the Whittaker model for principal series U(gl N)-modules, and its realization in the space of functions of totally positive unipotent matrices. In particular, our construction involves a representation theoretic derivation of the Batyrev-Ciocan-Fontanine-Kim-van Straten toric degeneration of Grm,N.

Ograniczanie wyników

3 Open Mathematics

2 Przebinda T.

1 Aubert A.-M.

1 Daszkiewicz A.

1 Oblezin S.

1 2014

1 2012

1 2007

The Cauchy Harish-Chandra Integral, for the pair $$\mathfrak{u}_{p,q} ,\mathfrak{u}_1 $$

A reverse engineering approach to the Weil representation

On parabolic Whittaker functions II