Read Weyl Group Multiple Dirichlet Series: Type a Combinatorial Theory

Weyl Group Multiple Dirichlet Series: Type a Combinatorial Theory

Ben Brubaker

4.9/5 (13593 ratings)

Description:Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics.These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished.The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Weyl Group Multiple Dirichlet Series: Type a Combinatorial Theory. To get started finding Weyl Group Multiple Dirichlet Series: Type a Combinatorial Theory, you are right to find our website which has a comprehensive collection of manuals listed.
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Pages: 398

Format: PDF, EPUB & Kindle Edition

Publisher: N/A

Release: 2011

ISBN: 1400838991

Description: Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics.These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished.The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Weyl Group Multiple Dirichlet Series: Type a Combinatorial Theory. To get started finding Weyl Group Multiple Dirichlet Series: Type a Combinatorial Theory, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Weyl Group Multiple Dirichlet Series: Type a Combinatorial Theory

Weyl Group Multiple Dirichlet Series: Type a Combinatorial Theory

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