Metaplectic Whittaker Functions and Crystals of Type B

Brubaker, Ben; Bump, Daniel; Chinta, Gautam; Gunnells, Paul E.

doi:10.1007/978-0-8176-8334-4_4

Cited by 34 publications

(61 citation statements)

References 18 publications

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“…Partial progress has been made for types B r (n even), as discussed in Brubaker, Bump, Chinta and Gunnells [7] and for type C r (n odd), as discussed in Beineke, Brubaker and Frechette [2]. More precisely, the definition as given above for a particular decomposition Σ does conjecturally satisfy functional equations and matches an appropriate Whittaker coefficient, though the cited papers prove only special cases within the respective types.…”

Section: Crystal Graph Description Of the P-partmentioning

confidence: 99%

Weyl group multiple Dirichlet series, Eisenstein series and crystal bases

2011

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We show that the Whittaker coefficients of Borel Eisenstein series on the metaplectic covers of GLr+1 can be described as multiple Dirichlet series in r complex variables, whose coefficients are computed by attaching a number-theoretic quantity (a product of Gauss sums) to each vertex in a crystal graph. These Gauss sums depend on "string data" previously introduced in work of Lusztig, Berenstein and Zelevinsky, and Littelmann. These data are the lengths of segments in a path from the given vertex to the vertex of lowest weight, depending on a factorization of the long Weyl group element into simple reflections. The coefficients may also be described as sums over strict Gelfand-Tsetlin patterns. The description is uniform in the degree of the metaplectic cover.

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Section: Crystal Graph Description Of the P-partmentioning

confidence: 99%

Weyl group multiple Dirichlet series, Eisenstein series and crystal bases

2011

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“…There is also an application to the correlation functions in [18]). This observation triggered studies on finding various generalizations and variations of the Tokuyama-type formula for symmetric functions [19][20][21][22][23][24][25][26][27] such as the factorial Schur functions and symplectic Schur functions, and an interesting notion was introduced furthermore which the number theorists call it the metaplectic ice.…”

Section: Introductionmentioning

confidence: 99%

Izergin-Korepin Analysis on the Projected Wavefunctions of the Generalized Free-Fermion Model

Motegi

2017

Advances in Mathematical Physics

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We apply the Izergin-Korepin analysis to the study of the projected wavefunctions of the generalized free-fermion model. We introduce a generalization of the -operator of the six-vertex model by Bump-Brubaker-Friedberg and Bump-McNamara-Nakasuji. We make the Izergin-Korepin analysis to characterize the projected wavefunctions and show that they can be expressed as a product of factors and certain symmetric functions which generalizes the factorial Schur functions. This result can be seen as a generalization of the Tokuyama formula for the factorial Schur functions.

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“…For general even n, the representation is conjectural, and even in the n = 2 case there is still work to be done. See [10], this volume, for the case n = 2.…”

Section: Chinta-gunnellsmentioning

confidence: 99%

“…See [10] another application of the free-fermionic Yang-Baxter equation to metaplectic Whittaker functions, this time on the double cover of Sp(2r).…”

Section: Chinta-gunnellsmentioning

confidence: 99%