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Level One Algebraic Cusp Forms of Classical Groups of Small Rank

2015 Cusp forms (Mathematics)
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Release : 2015
Genre : Cusp forms (Mathematics)
Kind : eBook
Book Rating : 098/5 ( reviews)

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Book Synopsis Level One Algebraic Cusp Forms of Classical Groups of Small Rank by : Gaëtan Chenevier

Download or read book Level One Algebraic Cusp Forms of Classical Groups of Small Rank written by Gaëtan Chenevier. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of \mathrm{GL}_n over \mathbb Q of any given infinitesimal character, for essentially all n \leq 8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple \mathbb Z-forms of the compact groups \mathrm{SO}_7, \mathrm{SO}_8, \mathrm{SO}_9 (and {\mathrm G}_2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level o.

Level One Algebraic Cusp Forms of Classical Groups of Small Rank

2015-08-21 Mathematics
Download Level One Algebraic Cusp Forms of Classical Groups of Small Rank PDF Online Free

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Release : 2015-08-21
Genre : Mathematics
Kind : eBook
Book Rating : 94X/5 ( reviews)

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Book Synopsis Level One Algebraic Cusp Forms of Classical Groups of Small Rank by : Gaëtan Chenevier

Download or read book Level One Algebraic Cusp Forms of Classical Groups of Small Rank written by Gaëtan Chenevier. This book was released on 2015-08-21. Available in PDF, EPUB and Kindle. Book excerpt: The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.

Symmetry Breaking for Representations of Rank One Orthogonal Groups

2015-10-27 Mathematics
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Release : 2015-10-27
Genre : Mathematics
Kind : eBook
Book Rating : 22X/5 ( reviews)

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Book Synopsis Symmetry Breaking for Representations of Rank One Orthogonal Groups by : Toshiyuki Kobayashi

Download or read book Symmetry Breaking for Representations of Rank One Orthogonal Groups written by Toshiyuki Kobayashi. This book was released on 2015-10-27. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of and . They construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explicitly. Symmetry breaking operators at exceptional discrete parameters are thoroughly studied. The authors obtain closed formulae for the functional equations which the composition of the symmetry breaking operators with the Knapp-Stein intertwining operators of and satisfy, and use them to determine the symmetry breaking operators between irreducible composition factors of the spherical principal series representations of and . Some applications are included.

Irreducible Geometric Subgroups of Classical Algebraic Groups

2016-01-25 Mathematics
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Release : 2016-01-25
Genre : Mathematics
Kind : eBook
Book Rating : 945/5 ( reviews)

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Book Synopsis Irreducible Geometric Subgroups of Classical Algebraic Groups by : Timothy C. Burness,

Download or read book Irreducible Geometric Subgroups of Classical Algebraic Groups written by Timothy C. Burness,. This book was released on 2016-01-25. Available in PDF, EPUB and Kindle. Book excerpt: Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .

Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4

2016-01-25 Mathematics
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Release : 2016-01-25
Genre : Mathematics
Kind : eBook
Book Rating : 488/5 ( reviews)

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Book Synopsis Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4 by : Bob Oliver

Download or read book Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4 written by Bob Oliver. This book was released on 2016-01-25. Available in PDF, EPUB and Kindle. Book excerpt: The author classifies all reduced, indecomposable fusion systems over finite -groups of sectional rank at most . The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional -rank at most . But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

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