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Showing 1 to 20 of 20 for “"Reductive group"”.
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Del Pezzo surfaces with irregularity and intersection numbers on quotients in geometric invariant theory
… Pezzo surfaces for which the first cohomology group of the structure sheaf is nonzero. Such surfaces, which only exist over imperfect fields, arise as generic fibres of fibrations of singular del Pezzo surfaces in positive characteristic whose total spaces are smooth, and their study is …
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Branching from K to M for split classical groups
… solve branching from K to M for the real split reductive group of type A, one inductive and one related to semistandard Young tableaux. The results extend to branching from Ke to M Ke for the real split reductive groups of type Bn and Dn.
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Parabolic Springer resolution
Let G be a reductive group over a field k = k. Let P be a parabolic subgroup. We construct a functor Groupoid ... is a connected space, which induces an action of generalizing a classical result. It is also a part of a study of natural equivalences between ... for P, Q associated parabolic …
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Endoscopy for affine Hecke categories
… of the affine monodromic Hecke category for a reductive group is monoidally equivalent to the neutral block of the affine Hecke category for the endoscopic group. The semisimple complexes of both categories can be identified with the generalized Soergel bimodules via the Soergel functor. We …
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Nearby cycles and the cohomology of shtukas
… parameters from automorphic forms for any reductive group over a function field using excursion operators. Our aim is to give a general approach for proving certain local-global compatibilities satisfied by these Langlands parameters. The main consequence for the Langlands correspondence is …
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SUPERCUSPIDAL REPRESENTATIONS ARISING FROM STABLE VECTORS
For a reductive group $G$ over a $p$-adic field $k$, one may grade the associated Lie algebra $\g$ by an automorphism of order $m$. It has been shown that stable vectors $v\in\g_{a}$ arise only when $a$ is coprime to $m$. Given a stable vector $v\in\g_{a}$, we construct packets of supercuspidal …
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The unramified principal series of p-adic groups : the Bessel function
Let G be a connected reductive group with a split maximal torus defined over a nonarchimedean local field. I evaluate a matrix coefficient of the unramified principal series of G known as the "Bessel function" at torus elements of dominant coweight. I show that the Bessel function shares many …
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Eigenvarieties and twisted eigenvarieties
For an arbitrary reductive group G, we construct the full eigenvariety E, which parameterizes all p-adic overconvergent cohomological eigenforms of G in the sense of Ash-Stevens and Urban. Further, given an algebraic automorphism a of G, we construct the twisted eigenvariety E^a, a rigid subspace …
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On affine embeddings of reductive groups
… the case of affine normal embeddings of reductive groups. We might guess that as in the case of toric varieties, some specific subset of one-parameter subgroups may contribute to the classification of affine embeddings of general reductive group. To check this, we review the theory of …
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On the signature of the Shapovalov form
… irreducible unitary representations of a real reductive group is equivalent to the algebraic problem of classifying the Harish-Chandra modules admitting a positive definite invariant Hermitian form. Finding a formula for the signature of the Shapovalov form is a related problem which may be a …
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Affine Springer Fibers and the Kazhdan-Lusztig Map
Let G be a connected reductive group with Lie algebra g and Weyl group W. Let P ⊂ G((t)) be a parahoric subgroup with Levi quotient Gₚ. Using the topology of Lie P, Kazhdan and Lusztig define a map from nilpotent orbits in Lie Gₚ to conjugacy classes in W. This thesis proves compatibilities between …
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p-arithmetic cohomology and p-adic automorphic forms
The cohomology of an arithmetic group with coefficients in finite-dimensional representations can be described in terms of automorphic representations of the group. In this thesis, we prove similar results for the cohomology of an *S*-arithmetic groups (where *S* is a finite set of primes) with …
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Unipotent representations of real reductive groups
Let G be a real reductive group and let Ĝ be the set of irreducible unitary representations of G. The determination of Ĝ (for arbitrary G) is one of the fundamental unsolved problems in representation theory. In the early 1980s, Arthur introduced a finite set Unip(G) of (conjecturally unitary) …
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Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory
… p]-cohomology of the classifying stack of a reductive group, compute the ring of prismatic characteristic classes at non-torsion primes and give some new examples of the Hodge-to-de Rham degeneration for stacks in characteristic 0. We also study some descent properties of certain Brauer group …
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Positive traces and analytic Langlands correspondence
… irreducible unitary representations of real reductive Lie groups. We consider the case of Kleinian singularities of type A and provide a complete classification of positive traces. The second direction is analytic Langlands correspondence, which is the following. Let X be a smooth irreducible …
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Some results related to the quantum geometric Langlands program
… perverse sheaves on the affine Grassmannian of a reductive group G and the category of representations of its Langlands dual group. The category of spherical perverse sheaves sits naturally in an equivariant derived category, and this larger category was described in terms of the dual group by …
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The Taylor-Wiles method for reductive groups
… Galois representations ρ valued in an arbitrary reductive group Ĝ which we use to develop a variant of the Taylor–Wiles method. Our generalization allows Taylor–Wiles places for which the image of Frobenius is semisimple, a weakening of the regular semisimple constraint imposed previously in the …
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Types and supercuspidal representations of p-adic symplectic groups
… = <b>G</b>(<i>F</i>) be the <i>F</i>-points of a reductive group defined over <i>F</i>. Bushnell and Kutzko have described a strategy to classify the representations of <i>G</i> via the theory of types, which associates to each inertial class in the Bernstein spectrum a pair (<i>K</i>, ρ) …
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Kazhdan-Laumon Categories and Representations
… category, an abelian category A associated to a reductive group G over a finite field, with the aim of using it to construct discrete series representations of the finite Chevalley group G(F subscript q). The welldefinedness of their construction depended on their conjecture that this category …
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Kategorielle Langlands-Korrespondenz für die verallgemeinerten Lorentz-Gruppen
Im Rahmen der lokalen Langlands-Philosophie für die reellen Zahlen konstruieren Adams, Barbasch und Vogan eine Bijektion zwischen den einfachen Harish-Chandra-Moduln zu einer reellen reduktiven Gruppe G und dem Raum <br>der "vollständigen geometrischen Parameter" - einer Menge von äquivarianten …