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Record Nr. |
UNINA9910459795903321 |
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Autore |
Brubaker Ben <1976-> |
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Titolo |
Weyl group multiple Dirichlet [[electronic resource] /] / Ben Brubaker, Daniel Bump, and Solomon Friedberg |
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Pubbl/distr/stampa |
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Princeton, N.J., : Princeton University Press, c2011 |
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ISBN |
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1-283-01338-X |
9786613013385 |
1-4008-3899-1 |
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Edizione |
[Course Book] |
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Descrizione fisica |
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1 online resource (173 p.) |
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Collana |
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Annals of mathematics studies ; ; no. 175 |
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Altri autori (Persone) |
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BumpDaniel <1952-> |
FriedbergSolomon <1958-> |
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Disciplina |
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Soggetti |
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Dirichlet series |
Weyl groups |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Front matter -- Contents -- Preface -- Chapter One. Type A Weyl Group Multiple Dirichlet Series -- Chapter Two. Crystals and Gelfand-Tsetlin Patterns -- Chapter Three. Duality -- Chapter Four. Whittaker Functions -- Chapter Five. Tokuyama's Theorem -- Chapter Six. Outline of the Proof -- Chapter Seven. Statement B Implies Statement A -- Chapter Eight. Cartoons -- Chapter Nine. Snakes -- Chapter Ten. Noncritical Resonances -- Chapter Eleven. Types -- Chapter Twelve. Knowability -- Chapter Thirteen. The Reduction to Statement D -- Chapter Fourteen. Statement E Implies Statement D -- Chapter Fifteen. Evaluation of ΛΓ and ΛΔ, and Statement G -- Chapter Sixteen. Concurrence -- Chapter Seventeen. Conclusion of the Proof -- Chapter Eighteen. Statement B and Crystal Graphs -- Chapter Nineteen. Statement B and the Yang-Baxter Equation -- Chapter Twenty. Crystals and p-adic Integration -- Bibliography -- Notation -- Index |
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Sommario/riassunto |
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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 |
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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. |
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2. |
Record Nr. |
UNINA9910452566503321 |
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Titolo |
The Vicksburg Campaign, March 29-May 18, 1863 / / edited by Steven E. Woodworth and Charles D. Grear |
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Pubbl/distr/stampa |
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Carbondale : , : Southern Illinois University Press, , [2013] |
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©2013 |
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ISBN |
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Descrizione fisica |
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1 online resource (268 p.) |
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Collana |
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Civil War campaigns in the heartland |
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Altri autori (Persone) |
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WoodworthSteven E |
GrearCharles D. <1976-> |
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Disciplina |
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Soggetti |
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Electronic books. |
Vicksburg (Miss.) History Siege, 1863 |
Mississippi History Civil War, 1861-1865 Campaigns |
United States History Civil War, 1861-1865 Campaigns |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Running the gauntlet: the effectiveness of combined forces in the Vicksburg Campaign / Gary D. Joiner -- "Through the heart of rebel country": the history and memory of Grierson's Raid / Charles D. Grear -- "In the enemy's country": Port Gibson and the turning point of the Vicksburg Campaign / Jason M. Frawley -- Roads to Raymond / J. Parker Hills -- The first capture and occupation of Jackson, Mississippi / Steven E. Woodworth -- "I am too late": Joseph E. Johnston and the Vicksburg Campaign / John R. Lundberg -- Grant, McClernand, and Vicksburg: a clash of personalities and backgrounds / Michael B. Ballard -- "Developed by circumstances": Grant, intelligence, and the Vicksburg Campaign / William B. Feis -- "A victory could hardly have been more complete": the Battle of Big Black River Bridge / Timothy B. Smith -- The "stealing tour": soldiers and civilians in Grant's march to Vicksburg / Steven Nathaniel Dossman -- Politics, policy, and General Grant: Clausewitz on the operational art as practiced in the Vicksburg Campaign / Paul L. Schmelzer. |
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