A natural orthogonal basis of eigenfunctions of the Hecke algebra acting on Cayley graphs
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- by Jing Hua Kuang PDF
- Proc. Amer. Math. Soc. 123 (1995), 3615-3622 Request permission
Abstract:
This paper discusses the representation of the Hecke algebra of ${\text {GL}_2}({\mathbb {F}_q})$ on a class of Cayley graphs and gives a natural construction of an orthogonal basis of simultaneous eigenfunctions whose eigenvalues are the Soto-Andrade Sums.References
- Ronald Evans, Character sums as orthogonal eigenfunctions of adjacency operators for Cayley graphs, Finite fields: theory, applications, and algorithms (Las Vegas, NV, 1993) Contemp. Math., vol. 168, Amer. Math. Soc., Providence, RI, 1994, pp. 33–50. MR 1291416, DOI 10.1090/conm/168/01687
- Nicholas M. Katz, Estimates for Soto-Andrade sums, J. Reine Angew. Math. 438 (1993), 143–161. MR 1215651, DOI 10.1515/crll.1993.438.143
- Aloys Krieg, Hecke algebras, Mem. Amer. Math. Soc. 87 (1990), no. 435, x+158. MR 1027069, DOI 10.1090/memo/0435 W. Li, A survey of Ramanujan graphs, Proc. Conf. on Arithmetic Geometry and Coding Theory at Luminy, 1993.
- Jorge Soto-Andrade, Geometrical Gel′fand models, tensor quotients, and Weil representations, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 305–316. MR 933420
- Ilya Piatetski-Shapiro, Complex representations of $\textrm {GL}(2,\,K)$ for finite fields $K$, Contemporary Mathematics, vol. 16, American Mathematical Society, Providence, R.I., 1983. MR 696772
- Jeff Angel, Nancy Celniker, Steve Poulos, Audrey Terras, Cindy Trimble, and Elinor Velasquez, Special functions on finite upper half planes, Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991) Contemp. Math., vol. 138, Amer. Math. Soc., Providence, RI, 1992, pp. 1–26. MR 1199118, DOI 10.1090/conm/138/1199118
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3615-3622
- MSC: Primary 11L99; Secondary 05C25, 11F25, 20G05
- DOI: https://doi.org/10.1090/S0002-9939-1995-1301511-5
- MathSciNet review: 1301511