• Corpus ID: 229924380

Metaplectic Iwahori Whittaker functions and supersymmetric lattice models

@inproceedings{Brubaker2020MetaplecticIW,
  title={Metaplectic Iwahori Whittaker functions and supersymmetric lattice models},
  author={Ben Brubaker and Valentin Buciumas and Daniel Bump and Henrik P. A. Gustafsson},
  year={2020}
}
In this paper we consider Iwahori Whittaker functions on n-fold metaplectic covers G̃ of G(F ) with G a split reductive group over a non-archimedean local field F . For every element φ of a basis of Iwahori Whittaker functions, and for every g ∈ G̃, we evaluate φ(g) by recurrence relations over the Weyl group using “vector Demazure-Whittaker operators.” Specializing to the case of G = GLr, we exhibit a solvable lattice model whose partition function equals φ(g). These models are of a new type… 
5 Citations
A Lattice Model for Super LLT Polynomials
We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock
Combinatorics of Iwahori Whittaker Functions
We give a combinatorial evaluation of Iwahori Whittaker functions for unramified genuine principal series representations on metaplectic covers of the general linear group over a non-archimedean
Iwahori-metaplectic duality
Let F be a nonarchimedean local field. It is shown in earlier work that both spherical Whittaker functions on the metaplectic n-fold cover of GLr(F ) and Iwahori Whittaker functions on GLr(F ) may be
Lattice Models, Hamiltonian Operators, and Symmetric Functions
We give general conditions for the existence of a Hamiltonian operator whose discrete time evolution matches the partition function of certain solvable lattice models. In particular, we examine two
Stochastic symplectic ice
In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term “stochastic symplectic ice”. The models consist of alternating

References

SHOWING 1-10 OF 67 REFERENCES
Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials
We construct a family of representations of affine Hecke algebras, which depend on a number of auxiliary parameters $$g_i$$ g i , and which we refer to as metaplectic representations. We
Metaplectic representations of Hecke algebras
  • Weyl group actions, and associated polynomials
  • 2018
Constructing Weyl group multiple Dirichlet series
Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for Re(si) sufficiently large,
Quasi-Hopf $*$-Algebras
We introduce quasi-Hopf $*$-algebras i.e. quasi-Hopf algebras equipped with a conjugation (star) operation. The definition of quasi-Hopf $*$-algebras proposed ensures that the class of quasi-Hopf
Metaplectic forms
and M
  • Wheeler. Colored fermionic vertex models and symmetric functions
  • 2021
and H
  • P. A. Gustafsson. Colored vertex models and Iwahori Whittaker functions
  • 2019
On Iwahori–Whittaker functions for metaplectic groups
Abstract We relate Iwahori–Whittaker functions on metaplectic covers to certain Demazure–Lusztig operators, the latter of which are built from a Weyl group action previously considered by G. Chinta
Diagonalization of transfer matrix of supersymmetry $u_q(\hat{sl}(m+1|n+1))$ chain with a boundary
We study the supersymmetry $U_q(\hat{sl}(M+1|N+1))$ analogue of the supersymmetric t-J model with a boundary, in the framework of the algebraic analysis method. We diagonalize the commuting transfer
Principal Series Representations of Metaplectic Groups Over Local Fields
Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension \(\widetilde{G}\) of G by a cyclic group of order n, under
...
1
2
3
4
5
...