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Full-Text Articles in Physical Sciences and Mathematics
Crystal Graphs, Tokuyama's Theorem, And The Gindikin-Karpelevic Formula For G2, Holley Friedlander, Louis Gaudet, Paul E. Gunnells
Crystal Graphs, Tokuyama's Theorem, And The Gindikin-Karpelevic Formula For G2, Holley Friedlander, Louis Gaudet, Paul E. Gunnells
Paul Gunnells
We conjecture a deformation of the Weyl character formula for type G2 in the spirit of Tokuyama’s formula for type A . Using our conjecture, we prove a combinatorial version of the Gindikin–Karpelevič formula for G2 , in the spirit of Bump–Nakasuji’s formula for type A .
Kazhdan-Lusztig Cells In Planar Hyperbolic Coxeter Groups And Automata, Mikhail V. Belolipetsky, Paul E. Gunnells, Richard A. Scott
Kazhdan-Lusztig Cells In Planar Hyperbolic Coxeter Groups And Automata, Mikhail V. Belolipetsky, Paul E. Gunnells, Richard A. Scott
Paul Gunnells
Let C be a one- or two-sided Kazhdan–Lusztig cell in a Coxeter group (W, S), and let Red(C) be the set of reduced expressions of all w ∈ C, regarded as a language over the alphabet S. Casselman has conjectured that Red(C) is regular. In this paper, we give a conjectural description of the cells when W is the group corresponding to a hyperbolic polygon, and show that our conjectures imply Casselman's.
Mod 2 Homology For Gl(4) And Galois Representations, Avner Ash, Paul E. Gunnells, Mark Mcconnell
Mod 2 Homology For Gl(4) And Galois Representations, Avner Ash, Paul E. Gunnells, Mark Mcconnell
Paul Gunnells
We extend the computations in [AGM11] to find the mod 2 homology in degree 1 of a congruence subgroup Γ of SL(4,Z) with coefficients in the sharbly complex, along with the action of the Hecke algebra. This homology group is related to the cohomology of Γ with F2 coefficients in the top cuspidal degree. These computations require a modification of the algorithm to compute the action of the Hecke operators, whose previous versions required division by 2. We verify experimentally that every mod 2 Hecke eigenclass found appears to have an attached Galois representation, giving evidence for a conjecture in …
A Table Of Elliptic Curves Over The Cubic Field Of Discriminant −23, Steve Donnelly, Paul Gunnells, Ariah Klages-Mundt, Dan Yasaki
A Table Of Elliptic Curves Over The Cubic Field Of Discriminant −23, Steve Donnelly, Paul Gunnells, Ariah Klages-Mundt, Dan Yasaki
Paul Gunnells
Abstract. Let F be the cubic field of discriminant −23 and OF its ring of integers. Let be the arithmetic group GL2(OF ), and for any ideal n ⊂ OF let 0(n) be the congruence subgroup of level n. In [16], two of us (PG and DY) computed the cohomology of various 0(n), along with the action of the Hecke operators. The goal of [16] was to test the modularity of elliptic curves over F. In the present paper, we complement and extend the results of [16] in two ways. First, we tabulate more elliptic curves than were found …
Metaplectic Demazure Operators And Whittaker Functions, Gautam Chinta, Paul Gunnells, Anna Pusk´As
Metaplectic Demazure Operators And Whittaker Functions, Gautam Chinta, Paul Gunnells, Anna Pusk´As
Paul Gunnells
Abstract. In [CG10] the first two named authors defined an action of a Weyl group on rational functions and used it to construct multiple Dirichlet series. These series are related to Whittaker functions on an n-fold metaplectic cover of a reductive group. In this paper, we define metaplectic analogues of the Demazure and Demazure-Lusztig operators. We show how these operators can be used to recover the formulas from [CG10], and how, together with results of McNamara [McN], they can be used to compute Whittaker functions on metaplectic groups over p-adic fields.