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1 
The genus and localization of groupsO'Sullivan, Niamh Eleanor January 1996 (has links)
No description available.

2 
Covering and sheaf theories on module categoriesSayer, Richard Michael Paul January 1998 (has links)
No description available.

3 
Representations of the symmetric groupsScopes, Joanna January 1990 (has links)
No description available.

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Generalized CalogeroMoser spaces and rational Cherednik algebrasBellamy, Gwyn January 2010 (has links)
The subject of this thesis is the interplay between the geometry and the representation theory of rational Cherednik algebras at t = 0. Exploiting this relationship, we use representation theoretic techniques to classify all complex re ection groups for which the geometric space associated to a rational Cherednik algebra, the generalized CalogeroMoser space, is singular. Applying results of GinzburgKaledin and Namikawa, this classification allows us to deduce a (nearly complete) classification of those symplectic reflection groups for which there exist crepant resolutions of the corresponding symplectic quotient singularity. Then we explore a particular way of relating the representation theory and geometry of a rational Cherednik algebra associated to a group W to the representation theory and geometry of a rational Cherednik algebra associated to a parabolic subgroup of W. The key result that makes this construction possible is a recent result of Bezrukavnikov and Etingof on completions of rational Cherednik algebras. This leads to the definition of cuspidal representations and we show that it is possible to reduce the problem of studying all the simple modules of the rational Cherednik algebra to the study of these nitely many cuspidal modules. We also look at how the EtingofGinzburg sheaf on the generalized CalogeroMoser space can be "factored" in terms of parabolic subgroups when it is restricted to particular subvarieties. In particular, we are able to confirm a conjecture of Etingof and Ginzburg on "factorizations" of the EtingofGinzburg sheaf. Finally, we use Clifford theoretic techniques to show that it is possible to deduce the CalogeroMoser partition of the irreducible representations of the complex reflection groups G(m; d; n) from the corresponding partition for G(m; 1; n). This confirms, in the case W = G(m; d; n), a conjecture of Gordon and Martino relating the CalogeroMoser partition to Rouquier families for the corresponding cyclotomic Hecke algebra.

5 
Separating Sets for the Alternating and Dihedral GroupsBanister, Melissa 01 January 2004 (has links)
This thesis presents the results of an investigation into the representation theory of the alternating and dihedral groups and explores how their irreducible representations can be distinguished with the use of class sums.

6 
Some results in Iwasawa Theory and the padic representation theory of padic GL₂Kidwell, Keenan James 25 June 2014 (has links)
This thesis is divided into two parts. In the first, we generalize results of GreenbergVatsal on the behavior of algebraic lambdainvariants of pordinary modular forms under congruence. In the second, we generalize a result of Emerton on maps between locally algebraic parabolically induced representations and unitary Banach space representations of GL₂ over a padic field. / text

7 
Embeddings of flag manifolds and cohomological components of modulesTSANOV, VALDEMAR VASILEV 23 August 2011 (has links)
This thesis is a study in Representation Theory and Geometry. These two branches of mathematics have a fruitful interaction, with many applications to Physics and other sciences. Central objects of interest are homogeneous spaces and their symmetry groups. The geometric and analytic properties of homogeneous spaces relate to the structure and representation theory of the corresponding groups. The focus of this work is on certain representation theoretic phenomena related to equivariant embeddings of homogeneous spaces.
The BorelWeilBott theorem, a milestone in Representation Theory and Geometry, provides realizations for every irreducible module of a semisimple complex Lie group as various cohomology spaces of homogeneous vector bundles on flag manifolds of the group. The purpose of this dissertation is to initiate a study of the behaviour of the BorelWeilBott construction under pullbacks along equivariant embeddings of flag manifolds. These pullbacks provide certain geometric branching rules for representations. This is where the notion of a cohomological component arises from.
The central result of the dissertation is a criterion for nonvanishing of the pullback. The framework used for the formulation and proof of the result is Kostant's theory of Lie algebra cohomology. After the general criterion is established, various specializations and applications are presented: special classes of embeddings are considered, for which the criterion takes simpler forms; relations are established between pullbacks along embeddings of complete and partial flag manifolds; properties of the set of cohomological components are obtained; various examples are considered, the most interesting of which is related to the theory of invariants of semisimple Lie algebras. / Thesis (Ph.D, Mathematics & Statistics)  Queen's University, 20110823 11:55:57.845

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Lie Algebras and Representation TheoryCarr, Andrew Nickolas 01 August 2016 (has links)
The purpose of this paper is to introduce the reader to Lie algebras and representation theory.

9 
Representations of KhovanovLaudaRouquier algebras of affine Lie typeMuth, Robert 27 October 2016 (has links)
We study representations of KhovanovLaudaRouquier (KLR) algebras of affine Lie type. Associated to every convex preorder on the set of positive roots is a system of cuspidal modules for the KLR algebra. For a balanced order, we study imaginary semicuspidal modules by means of `imaginary SchurWeyl duality'. We then generalize this theory from balanced to arbitrary convex preorders for affine ADE types. Under the assumption that the characteristic of the ground field is greater than some explicit bound, we prove that KLR algebras are properly stratified. We introduce affine zigzag algebras and prove that these are Morita equivalent to arbitrary imaginary strata if the characteristic of the ground field is greater than the bound mentioned above. Finally, working in finite or affine affine type A, we show that skew Specht modules may be defined over the KLR algebra, and real cuspidal modules associated to a balanced convex preorder are skew Specht modules for certain explicit hook shapes.

10 
Relations in the Witt Group of Nondegenerate Braided Fusion Categories Arising from the Representation Theory of Quantum Groups at Roots of UnitySchopieray, Andrew 06 September 2017 (has links)
For each finite dimensional Lie algebra $\mathfrak{g}$ and positive integer $k$ there exists a modular tensor category $\mathcal{C}(\mathfrak{g},k)$ consisting of highest weight integrable $\hat{\mathfrak{g}}$modules of level $k$ where $\hat{\mathfrak{g}}$ is the corresponding affine Lie algebra. Relations between the classes $[\mathcal{C}(\mathfrak{sl}_2,k)]$ in the Witt group of nondegenerate braided fusion categories have been completely described in the work of Davydov, Nikshych, and Ostrik. Here we give a complete classification of relations between the classes $[\mathcal{C}(\mathfrak{sl}_3,k)]$ relying on the classification of conncted \'etale alegbras in $\mathcal(\mathfrak_3,k)$ ($SU(3)$ modular invariants) given by Gannon. We then give an upper bound on the levels for which exceptional connected \'etale algebras may exist in the remaining rank 2 cases ($\mathcal{C}(\mathfrak{so}_5,k)$ and $\mathcal{C}(\mathfrak{g}_2,k)$) in hopes of a future classification of Witt group relations among the classes $[\mathcal{C}(\mathfrak{so}_5,k)]$ and $[\mathcal{C}(\mathfrak{g}_2,k)]$. This dissertation contains previously published material.

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