4,362 research outputs found
Evaluating Jacquet's GL(n) Whittaker function
No full textAlgorithms for the explicit symbolic and numeric evaluation of Jacquet's Whittaker function for the GL(n,R)based generalized upper half-plane for n≥2, and an implementation for symbolic evaluation in the Mathematica package GL(n)pack, are described. This requires a comparison of the different definitions of Whittaker function which have appeared in the literature
Metaplectic Iwahori-Whittaker functions and Demazure-Lusztig operators
No full textMetaplectic Demazure-Lusztig operators are built on the Chinta-Gunnells action, and (analogously to their nonmetaplectic counterparts) are useful in the study of -adic (metaplectic) Whittaker functions. In this talk, I will present joint work with Manish Patnaik that relates metaplectic Iwahori-Whittaker functions to these operators directly. This process gives a metaplectic analogue of earlier work of Brubaker-Bump-Licata in the nonmetaplectic setting. I will also talk about combinatorics that allow the extension of relevant formulae to the affine Kac-Moody groups.Non UBCUnreviewedAuthor affiliation: University of AlbertaPostdoctora
Whittaker, I K, VX24
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/425554Surname: WHITTAKER. Given Name(s) or Initials: I K. Military Service Number or Last Known Location: VX24. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 9012.251615
Item: [2016.0049.57815] "Whittaker, I K, VX24
Whittaker Limits of Difference Spherical Functions
No full textThe q-Whittaker function is introduced as a limit at t = 0 of the global q, t-spherical function, which extends the symmetric Macdonald polynomials to arbitrary eigenvalues. The limiting procedure generalizes that due to Etingof. The construction heavily depends on the technique of the q-Gaussians developed by the author (and Stokman in the non-reduced case). In this approach, the q-Whittaker function is given by a series convergent everywhere. One of the applications is a q-version of the Shintani–Casselman–Shalika formula, which is directly connected with the q, t-Mehta–Macdonald identities in terms of the Jackson integral. In type A, this formula generalizes that due to Gerasimov et al. The Harish-Chandra-type asymptotic formula is established for the global q, t-spherical functions, including the Whittaker limit
Automorphic representations, Whittaker vectors, and black holes
No full textAutomorphic forms on exceptional Lie groups appear naturally in string theory compactifications.
They manifest themselves as couplings in higher derivative corrections and in terms of generating functions of black hole microstates. I will demonstrate how certain Fourier coefficients attached to the minimal automorphic representations of , , and are determined by maximally degenerate Whittaker vectors. This fact allows for a simple method for calculating explicit Fourier coefficients which are relevant in string theory. Various recent results, conjectures
and open problems are outlined.Non UBCUnreviewedAuthor affiliation: Chalmers University of TechnologyFacult
Whittaker Categories and Whittaker Modules for Lie Superalgebras
No full textFollowing analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, the construction of Whittaker modules from Whittaker modules for the even part. © 2014 Copyright Taylor & Francis Group, LLC
C. R. Whittaker, Herodian. Tome I. Books I-IV
No full textSchwartz Jacques. C. R. Whittaker, Herodian. Tome I. Books I-IV. In: L'antiquité classique, Tome 39, fasc. 1, 1970. pp. 230-231
C. R. Whittaker, Herodian. Tome I. Books I-IV
No full textSchwartz Jacques. C. R. Whittaker, Herodian. Tome I. Books I-IV. In: L'antiquité classique, Tome 39, fasc. 1, 1970. pp. 230-231
Kostant's problem for Whittaker modules
No full textWe study the classical problem of Kostant for Whittaker modules over Lie
algebras and Lie superalgebras. We give a sufficient condition for a positive
answer to Kostant's problem for the standard Whittaker modules over reductive
Lie algebras. Under the same condition, the positivity of the answer for simple
Whittaker modules is reduced to that for simple highest weight modules. We
develop several reduction results to reduce the Kostant's problem for standard
and simple Whittaker modules over a type I Lie superalgebra to that for the
corresponding Whittaker modules over the even part of this Lie superalgebra.Comment: 26 page
Canonical extension of Whittaker distributions for GL(n,R)
No full textThe “multiplicity one theorem” asserts that the space of Whittaker functionals on irreducible representations of GL(r, R) is at most one-dimensional. This was originally proven by Piatetski-Shapiro [10] and Shalika [11]. In [4], Kostant showed that the dimension of the space of Whittaker functionals for any principal series representation of a quasisplit linear Lie group is exactly one. We give a new proof of the existence of Whittaker functionals on the principal series representations of GL(n, R) by an explicit construction using the integration pairing of Whittaker distributions against smooth functions in the principal series representations. This pairing gives the Jacquet integral. We derive formulas for a change of variables in the integral, that enable us to compute the Jacquet integral directly by means of integration by parts and thereby prove its analytic continuation. This legitimizes the pairing of Whittaker distributions and smooth functions, hence proving the existence of Whittaker functionals.Ph.D.Includes bibliographical reference
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