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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 26 for “"Weyl group"”.
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Single-petaled K-types and Weyl group representations for classical groups
… quasi-single-petaled K-types for reductive Lie groups generalize petite K-types for split groups. First, we prove that a Weyl group algebra element represents the action of the long intertwining operator for each single-petaled K-type, and then we demonstrate that a Weyl group algebra element …
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A Hecke algebra quotient and properties of commutative elements of a Weyl group
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.
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A Combinatorially Explicit Relative Möbius Function on Affine Grassmannians and a Proposal for an Affine Infinite Symmetric Group
For an affine Weyl group W, we explicitly determine the elements for which the Möbius function of the subposet of affine Grassmannians under the Bruhat order is non-zero by utilizing the quantum Bruhat graph of the classical Weyl group associated to W . Then we examine embedding stable and …
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Extended affine lie algebras and extended affine weyl groups
… extended affine Lie algebras and extended affine Weyl groups. In Chapter I, we provide the basic knowledge necessary for the study of extended affine Lie algebras and related objects. In Chapter II, we show that the well-known twisting phenomena which appears in the realization of the twisted …
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The Combinatorial Curve Neighborhoods of Affine Flag Manifold in Type A<sub>n-1</sub><sup>(1)</sup>
… and let W<sub>aff</sub> be the associated affine Weyl group. The moment graph for X encodes the torus fixed points (which are elements of the affine Weyl group W<sub>aff</sub> and the torus stable curves in X. Given a fixed point u ∈ W<sub>aff</sub> and a degree d = (d₀, d₁, ..., d<sub>n−1</sub>) …
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On the signature of the Shapovalov form
… 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 necessary …
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Double Affine Bruhat Order
Given a finite Weyl group W_fin with root system Phi_fin, one can create the affine Weyl group W_aff by taking the semidirect product of the translation group associated to the coroot lattice for Phi_fin, with W_fin. The double affine Weyl semigroup W can be created by using a similar semidirect …
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On total Springer representations
… thesis studies the alternating sum of cohomology groups of a Springer fiber (in characteristic 0), called a total Springer representation, as a representation of both the Weyl group and the stabilizer of the corresponding nilpotent element. For classical types, we present explicit formulas for the …
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Classifying semisimple orbits of theta-groups
… of classifying the semisimple orbits of a theta-group. For this purpose, once a preliminary presentation of the theoretical subjects where my problem arises from, I first give an algorithm to compute a Cartan subspace; subsequently I describe how to compute the little Weyl group.
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Affine quantum algebras, Weyl groups and constructible functions
… In the first part we study the affine quantum group of type A, giving a geometric description of its natural inner product, and studying the theory of cells attached to the canonical basis. In the second part we study a realization of the group algebra of the Weyl group in a convolution algebra …
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Antilinear deformations of Coxeter groups with application to Hamiltonian systems
… The first method is based on any element of the Weyl group, which is extended to factorizations of the Coxeter element and a reduced Coxeter element thereafter. An antilinear deformation method for the longest element of the Weyl group is given as well. Our last construction method leads to an …
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Combinatorics in Schubert varieties and Specht modules
… varieties are parameterized by elements of the Weyl group. For each element of the Weyl group, we construct certain hyperplane arrangement. We show that the generating function for regions of this arrangement coincides with the Poincaré polynomial if and only if the Schubert variety is …
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Nilpotent orbits in bad characteristic and the Springer correspondence
Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p, g the Lie algebra of G and g* the dual vector space of g. This thesis is concerned with nilpotent orbits in g and g* and the Springer correspondence for g and g* when p is a bad prime. Denote W …
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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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A Bayesian approach to computing Brauer groups of cubic surfaces
We present an algorithm for computing the Brauer groups of cubic surfaces. The algorithm takes as input an equation for a cubic surface X and a confidence threshold 0.5 < r < 1 and outputs a candidate for the Brauer group of X and a confidence level > r for the result. The algorithm runs by …
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Multiplicative Global Springer Theory
… by constructing an action of the extended affine Weyl group on the cohomology of parabolic Hitchin fibers. Meanwhile, there is an ongoing program to replicate the theory of Higgs bundles for the multiplicative case. This involves the study of multiplicative affine Springer fibers, the …
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Descent Systems, Eulerian Polynomials and Toric Varieties
… of descent systems in the case of (W, S) finite Weyl group of type An and J combinatorially smooth of the following forms: 1. J = {s_1 , s_4 , s_5 , · · · , s_n } ⊂ S 2. J = {s_4 , s_5 , · · · , s_n } ⊂ S.
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Coxeter systems, multiplicity free representations, and twisted Kazhdan-Lusztig Theory
… systems, their Hecke algebras, and related groups. The first topic concerns the construction of generalized involution models, as defined by Bump and Ginzburg. We compute the automorphism groups of all complex reflection groups G(r, p, n) and using this information, we classify precisely …
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Dual Filtered Graphs for Kac-Moody algebras
… \Gamma_w(\Kcen))$ have the vertex set as the Weyl group of $g$, with the grading given by the length function. The edges of the graph $\Gamma_s(\La)$ are labeled versions of the $\lambda$-chain model of K-Chevalley rules for Kac-Moody flag manifolds as developed by Lenart and Shimozono, …
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On Projective Characters of Rotation Sub- Group
… in a £-dimensional real Euclidean space V with Weyl group W( £), and let W+{<f) denote its rotation subgroup. In [173 » the projective representations of the rotation subgroup W ( 9) have been determined from those of W( $) for each root system $. This is done by constructing non-trivial central …
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