Results 1 to 10 of about 13,441 (193)
Combinatorics of traces of Hecke operators. [PDF]
Proc Natl Acad Sci U S A, 2004 We investigate the combinatorial properties of the traces of the n th Hecke operators on the spaces of weight 2k cusp forms of level N . We establish examples in which these traces are expressed in terms of classical objects in enumerative combinatorics (e.g., tilings ...
Frechette S, Ono K, Papanikolas M.
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Hecke relations in rational conformal field theory
Journal of High Energy Physics, 2018 We define Hecke operators on vector-valued modular forms of the type that appear as characters of rational conformal field theories (RCFTs). These operators extend the previously studied Galois symmetry of the modular representation and fusion algebra of
Jeffrey A Harvey, Yuxiao Wu
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Application of automorphic forms to lattice problems
Journal of Mathematical Cryptology, 2022 In this article, we propose a new approach to the study of lattice problems used in cryptography. We specifically focus on module lattices of a fixed rank over some number field.
Düzlü Samed, Krämer Juliane
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Finiteness of cohomology groups of stacks of shtukas as modules over Hecke algebras, and applications [PDF]
Épijournal de Géométrie Algébrique, 2020 In this paper we prove that the cohomology groups with compact support of stacks of shtukas are modules of finite type over a Hecke algebra. As an application, we extend the construction of excursion operators, defined by V.
Cong Xue
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Solving the Bose-Hubbard model in new ways [PDF]
Quantum, 2022 We introduce a new method for analysing the Bose-Hubbard model for an array of bosons with nearest neighbor interactions. It is based on a number-theoretic implementation of the creation and annihilation operators that constitute the model.
Artur Sowa, Jonas Fransson
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Newton polygons of Hecke operators [PDF]
Annales mathématiques du Québec, 2020 In this computational paper we verify a truncated version of the Buzzard-Calegari conjecture on the Newton polygon of the Hecke operator $T_2$ for all large enough weights. We first develop a formula for computing $p$-adic valuations of exponential sums, which we then implement to compute $2$-adic valuations of traces of Hecke operators acting on ...
Chiriac, Liubomir, Jorza, Andrei
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Hecke group algebras as degenerate affine Hecke algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 The Hecke group algebra $\operatorname{H} \mathring{W}$ of a finite Coxeter group $\mathring{W}$, as introduced by the first and last author, is obtained from $\mathring{W}$ by gluing appropriately its $0$-Hecke algebra and its group algebra.
Florent Hivert +2 more
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The Classification of All Singular Nonsymmetric Macdonald Polynomials
Axioms, 2022 The affine Hecke algebra of type A has two parameters q,t and acts on polynomials in N variables. There are two important pairwise commuting sets of elements in the algebra: the Cherednik operators and the Jucys–Murphy elements whose simultaneous ...
Charles F. Dunkl
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GENERATING FUNCTIONS FOR HECKE OPERATORS [PDF]
International Journal of Number Theory, 2009 Fix a prime N, and consider the action of the Hecke operator TN on the space [Formula: see text] of modular forms of full level and varying weight κ. The coefficients of the matrix of TN with respect to the basis {E4i E6j | 4i + 6j = κ} for [Formula: see text] can be combined for varying κ into a generating function FN.
Al Hajj Shehadeh, Hala +2 more
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Series of the solutions to Yang–Baxter equations: Hecke type matrices and descendant R-, L-operators
Nuclear Physics B, 2018 We have constructed series of the spectral parameter dependent solutions to the Yang–Baxter equations defined on the tensor product of reducible representations with a symmetry of quantum (super)algebra.
Shahane A. Khachatryan
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