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Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Level One Algebraic Cusp Forms of Classical Groups of Small Rank PDF Author: Gaëtan Chenevier
Publisher: American Mathematical Soc.
ISBN: 147041094X
Category : Mathematics
Languages : en
Pages : 134

Book Description
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.

Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Level One Algebraic Cusp Forms of Classical Groups of Small Rank PDF Author: Gaëtan Chenevier
Publisher: American Mathematical Soc.
ISBN: 147041094X
Category : Mathematics
Languages : en
Pages : 134

Book Description
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.

Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Level One Algebraic Cusp Forms of Classical Groups of Small Rank PDF Author: Gaëtan Chenevier
Publisher:
ISBN: 9781470425098
Category : Cusp forms (Mathematics)
Languages : en
Pages : 122

Book Description
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.

Symmetry Breaking for Representations of Rank One Orthogonal Groups

Symmetry Breaking for Representations of Rank One Orthogonal Groups PDF Author: Toshiyuki Kobayashi
Publisher: American Mathematical Soc.
ISBN: 147041922X
Category : Mathematics
Languages : en
Pages : 124

Book Description
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

Irreducible Geometric Subgroups of Classical Algebraic Groups PDF Author: Timothy C. Burness,
Publisher: American Mathematical Soc.
ISBN: 1470414945
Category : Mathematics
Languages : en
Pages : 100

Book Description
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

Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4 PDF Author: Bob Oliver
Publisher: American Mathematical Soc.
ISBN: 1470415488
Category : Mathematics
Languages : en
Pages : 112

Book Description
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.

The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup

The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup PDF Author: U. Meierfrankenfeld
Publisher: American Mathematical Soc.
ISBN: 1470418770
Category : Mathematics
Languages : en
Pages : 356

Book Description
Let p be a prime, G a finite Kp-group S a Sylow p-subgroup of G and Q a large subgroup of G in S (i.e., CG(Q)≤Q and NG(U)≤NG(Q) for 1≠U≤CG(Q)). Let L be any subgroup of G with S≤L, Op(L)≠1 and Q⋬L. In this paper the authors determine the action of L on the largest elementary abelian normal p-reduced p-subgroup YL of L.

Nil Bohr-Sets and Almost Automorphy of Higher Order

Nil Bohr-Sets and Almost Automorphy of Higher Order PDF Author: Wen Huang
Publisher: American Mathematical Soc.
ISBN: 147041872X
Category : Mathematics
Languages : en
Pages : 98

Book Description
Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d∈N does the collection of {n∈Z:S∩(S−n)∩…∩(S−dn)≠∅} with S syndetic coincide with that of Nild Bohr0 -sets? In the second part, the notion of d -step almost automorphic systems with d∈N∪{∞} is introduced and investigated, which is the generalization of the classical almost automorphic ones.

Descent Construction for GSpin Groups

Descent Construction for GSpin Groups PDF Author: Joseph Hundley
Publisher: American Mathematical Soc.
ISBN: 1470416670
Category : Mathematics
Languages : en
Pages : 138

Book Description
In this paper the authors provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of essentially self-dual representations, that is, representations which are isomorphic to the twist of their own contragredient by some Hecke character. The authors' theory supplements the recent work of Asgari-Shahidi on the functorial lift from (split and quasisplit forms of) GSpin2n to GL2n.

Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations

Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations PDF Author: Genni Fragnelli
Publisher: American Mathematical Soc.
ISBN: 1470419548
Category : Mathematics
Languages : en
Pages : 96

Book Description
The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.

Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities

Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities PDF Author: Bart Bories
Publisher: American Mathematical Soc.
ISBN: 147041841X
Category : Mathematics
Languages : en
Pages : 146

Book Description
In 2011 Lemahieu and Van Proeyen proved the Monodromy Conjecture for the local topological zeta function of a non-degenerate surface singularity. The authors start from their work and obtain the same result for Igusa's p-adic and the motivic zeta function. In the p-adic case, this is, for a polynomial f∈Z[x,y,z] satisfying f(0,0,0)=0 and non-degenerate with respect to its Newton polyhedron, we show that every pole of the local p-adic zeta function of f induces an eigenvalue of the local monodromy of f at some point of f−1(0)⊂C3 close to the origin. Essentially the entire paper is dedicated to proving that, for f as above, certain candidate poles of Igusa's p-adic zeta function of f, arising from so-called B1-facets of the Newton polyhedron of f, are actually not poles. This turns out to be much harder than in the topological setting. The combinatorial proof is preceded by a study of the integral points in three-dimensional fundamental parallelepipeds. Together with the work of Lemahieu and Van Proeyen, this main result leads to the Monodromy Conjecture for the p-adic and motivic zeta function of a non-degenerate surface singularity.
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