Arithmetical Investigations: Representation Theory, by Shai M. J. Haran PDF

By Shai M. J. Haran

In this quantity the writer additional develops his philosophy of quantum interpolation among the genuine numbers and the p-adic numbers. The p-adic numbers comprise the p-adic integers Zp that are the inverse restrict of the finite earrings Z/pn. this provides upward push to a tree, and likelihood measures w on Zp correspond to Markov chains in this tree. From the tree constitution one obtains specific foundation for the Hilbert house L2(Zp,w). the true analogue of the p-adic integers is the period [-1,1], and a chance degree w on it supplies upward thrust to a different foundation for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For unique (gamma and beta) measures there's a "quantum" or "q-analogue" Markov chain, and a distinct foundation, that inside definite limits yield the genuine and the p-adic theories. this concept could be generalized variously. In illustration concept, it's the quantum basic linear staff GLn(q)that interpolates among the p-adic team GLn(Zp), and among its genuine (and advanced) analogue -the orthogonal On (and unitary Un )groups. there's a comparable quantum interpolation among the genuine and p-adic Fourier rework and among the true and p-adic (local unramified a part of) Tate thesis, and Weil particular sums.

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Arithmetical Investigations: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations (Lecture Notes in Mathematics) by Shai M. J. Haran


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