Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 21 for “"Hecke algebras"”.
-
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 …
-
On some generic representations of generic Hecke algebras.
On some generic representations of generic Hecke algebras.
-
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 …
-
Unitary representations of rational Cherednik algebras and Hecke algebras
… the lowest weight category of rational Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke …
-
Relating Thompson's group V to graphs of groups and Hecke algebras
… Inspired by the fact that directed graph $C^*$-algebras $C^*(G)$ have algebraic analogues in Leavitt path algebras $L_K(G)$, we define a Leavitt graph-of-groups algebra $L_K(\mathcal{G})$ for $\mathcal{G}$. We extend Leavitt path algebra results to $L_K(\mathcal{G})$, including uniqueness …
-
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 …
-
On complex reflection groups G(m, 1, r) and their Hecke algebras
… of any element in an Ariki-Koike algebra (the Hecke algebra of a G(m, 1, r)) can be determined by the character values of some special elements in the algebra. These special elements correspond to the reduced expressions, which are constructed by the algorithm, for some special conjugacy class …
-
The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups
For complex reductive Lie algebras g, the classical Harish-Chandra homomorphism allows to link irreducible finite dimensional representations of g to those of certain subalgebras l. The Casselman-Osborne theorem establishes an extension of this link to infinite dimensional irreducible …
-
On representations of rational Cherednik algebras
… the representation theory of rational Cherednik algebras: the refined filtration by supports for the category O and the Dunkl weight function. The refined filtration by supports provides an analogue for rational Cherednik algebras of the Harish-Chandra series appearing in the representation …
-
Combinatorics of determinantal identities
… representations of the symmetric group, and also Hecke algebras and their characters. We extend a result on immanants due to Goulden and Jackson to a quantum setting, and reprove certain combinatorial interpretations of the characters of Hecke algebras due to Ram and Remmel.
-
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 …
-
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 …
-
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 …
-
Coxeter systems, multiplicity free representations, and twisted Kazhdan-Lusztig Theory
… to the representations of Coxeter 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 …
-
Torsion Units of Integral Group Rings and Scheme Rings
We study torsion units of algebras over the ring of integers Z with nice bases. These include integral group rings, integral adjacency algebras of association schemes and integral C-algebras. Torsion units of group rings have been studied extensively since the 1960’s. Much of the attention has been …
-
Edge labellings of partially ordered sets
… have Sn EL-labellings and describe a type A 0-Hecke algebra action on their maximal chains. This action is local and the resulting representation of these Hecke algebras is closely related to the flag h-vector. We show that finite graded lattices of rank n, in particular, have such an action if …
-
Soergel Diagrammatics for Dihedral Groups
We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W, finite or infinite. The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The indecomposable Soergel bimodules are …
-
Knot Floer Homology and Categorification
… of twisted Soergel bimodules categorifies the Hecke algebra with an extra indeterminate and its inverse adjoined. The braid group action, which is defined via twisted Rouquier complexes, is simultaneously a natural extension of the knot Floer cube of resolutions and a mild modification of the …
-
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 …
-
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 …
Page 1 of 2