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Showing 1 to 20 of 28 for “"Hecke algebra"”.
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representations of hecke algebra of type a
… some new results about representations of the Hecke algebraHF,q(Sn) of type A. In the first part we define the decomposition numbers dλν to be the composition multiplicity of the irreducible module Dν in the Specht module Sλ. Then we compute the decomposition numbers dλν for all partitions of …
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Spherical Elements in the Affine Yokonuma-Hecke Algebra
In Chapter 1 we introduce the Yokonuma-Hecke Algebra and a Yokonuma-Hecke Algebra-module. In Chapter 2 we determine that the possible eigenvalues of particular elements in the Yokonuma-Hecke Algebra acting on the module. In Chapter 3 we find determine module subspaces and eigenspaces that are …
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A Coherent Categorification of the Asymptotic Affine Hecke Algebra
Kazhdan–Lusztig categorified the affine Hecke algebra H in terms of equivariant coherent sheaves on the Steinberg variety. Recently, Ben-Zvi–Chen–Helm–Nadler have applied the formalism of categorical traces to construct a "coherent Springer sheaf" on a moduli stack of Deligne–Langlands parameters …
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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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Explicit formulas for weighted orbital integrals for the inhomogeneous and semi-Lie arithmetic fundamental lemmas conjectured for the full spherical Hecke algebra
… to a statement holding for the full spherical Hecke algebra. In the same spirit, there is a recent conjectural generalization of the arithmetic fundamental lemma to the full spherical Hecke algebra. This paper formulates another analogous conjecture for the semi-Lie version of the arithmetic …
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Constructing Hecke-type Structures, their Representations and Applications
… concerned with the construction of a large Hecke-type structure called the double a�ne Q-dependent braid group. The signi�cance of this structure is that it is located at the top level of the hierarchy of all other structures that are known to be related to the braid group. In particular, as …
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Higher Specht Polynomials for Representations of Iwahori-Hecke Algebras
… of the higher Specht polynomials to the Hecke algebra 𝓗_𝑞(𝑆_𝑛). These polynomials form a basis of the coinvariant algebra 𝕮 with respect to the action of 𝑆_𝑛, and they will decompose 𝕮 into irreducible representations of the Hecke algebra. These irreducible representations are 𝑞-Specht …
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On homomorphisms between specht modules for the Ariki-Koike algebra
… theory of both the symmetric and Iwahori-Hecke algebras, and there is hence considerable interest in achieving a greater understanding of their structure. To this end, over the past thirty years there has been much study undertaken of the homomorphism spaces between these modules, with a …
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Towards a functor between affine and finite Hecke categories in type A
… of the coherent version of the affine Hecke category in type A to the finite constructible Hecke category, partly categorifying a certain natural homomorphism of the corresponding Hecke algebras. This homomorphism sends generators of the Bernstein's commutative subalgebra inside the …
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Double affine Hecke algebras and noncommutative geometry
In the first part we study Double Affine Hecke algebra of type An-1 which is important tool in the theory of orthogonal polynomials. We prove that the spherical subalgebra eH(t, 1)e of the Double Affine Hecke algebra H(t, 1) of type An-1 is an integral Cohen-Macaulay algebra isomorphic to the …
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Hecke-Algebren zu unimodularen und unitären Matrixgruppen über Dedekind-Ringen
In this thesis the structure of the Hecke algebras related to unimodular matrix groups over Dedekind domains and to unitary matrix groups over the ring of integers of an imaginary quadratic number field is being analysed. The first main result of the analysis of the unimodular groups over a …
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On trigonometric and elliptic Cherednik algebras
… study the trigonometric and elliptic Cherednik algebras. In the first part, we give a Lie-theoretic construction of the trigonometric Cherednik algebras of type BC,. We construct a functor from the category of Harish- Chandra modules of the symmetric pair of type AIII to the category of …
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Relating Thompson's group V to graphs of groups and Hecke algebras
… Pask, Spielberg and Thomas constructed a $C^*$-algebra for a graph of groups, writtten $C^*(\mathcal{G})$, which bears many similarities to the $C^*$-algebra of a directed graph $G$. Inspired by the fact that directed graph $C^*$-algebras $C^*(G)$ have algebraic analogues in Leavitt path …
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Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras
… versions of "categorification" of the affine Hecke algebra and its periodic module: the first is by equivariant coherent sheaves on the Grothendieck resolution (and related objects), the second is by certain classes on bimodules over polynomial rings, called Soergel bimodules, and the third is …
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On the mod-p representations of unramified U(2,1)
… the simple modules of the pro-p Iwahori-Hecke algebra of G and described the so-called supersingular ones, which is one-dimensional character. Secondly, for the hyperspecial maximal compact open subgroup K0 of G and any irreducible smooth representation � of K0, and for any nonzero � 2 ~E …
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Universal polynomials in lambda rings and the K-theory of the infinite loop space tmf
The algebraic structure of the K-theory of a topological space is described by the more general notion of a lambda ring. We show how computations in a lambda ring are facilitated by the use of Adams operations, which are ring homomorphisms, and apply this principle to understand the algebraic …
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On conjectures related to character varieties of knots and Jones polynomials
… becomes a module over a certain Double Affine Hecke Algebra, from which they defined a family of polynomials J_n(K; q; t_1; t_2) generalizing the classical polynomials of Jones. In this thesis an analogue of Habiro’s cyclotomic equation for the J_n(K; q) is discovered for J_n(K; q; t_1; t_2). …
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On Using Graphical Calculi: Centers, Zeroth Hochschild Homology and Possible Compositions of Induction and Restriction Functors in Various Diagrammatical Algebras
… we compute the dimension of the center of the 0-Hecke algebra Hn and of the Nilcoxeter algebra NCn using a calculus of diagrams on the Moebius band. In the case of the Nilcoxeter algebra, this calculus is shown to produce a basis for Z(NCn) and the table of multiplication in this basis is shown …
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Quantized multiplicative quiver varieties and actions of higher genus braid groups
In this thesis, a new class of algebras called quantized multiplicative quiver varieties A (Q), is constructed, depending upon a quiver Q, its dimension vector d, and a certain "moment map" parameter . The algebras Ad(Q) are obtained via quantum Hamiltonian reduction of another algebra D,(Matd(Q)) …
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Knot Floer Homology and Categorification
… by Ozsváth and Szabó;, we first give a purely algebraic proof of invariance that does not depend on Heegaard diagrams, holomorphic disks, or grid diagrams. Then, taking Khovanov's HOMFLY-PT homology as our model, we define a category of twisted Soergel bimodules and construct a braid group …
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