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Showing 1 to 20 of 144 for “"REPRESENTATION THEORY"”.
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The representation theory of diagram algebras
In this thesis we study the modular representation theory of diagram algebras, in particular the Brauer and partition algebras, along with a brief consideration of the Temperley-Lieb algebra. The representation theory of these algebras in characteristic zero is well understood, and we show that it …
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Three topics in combinatorial representation theory
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms
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Generalized Whittaker vectors and representation theory.
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979.
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On the representation theory of persistence modules
In this thesis we study representation theoretic aspects of persistence modules. The first subject is an investigation of the spectrum of the category of vector space representations of a totally ordered set $T$: We show the existence of and determine the spectrum of this category in the sense of …
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Quantum Codes, Transversal Gates, and Representation Theory
… t-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the Knill-Laflamme error correction conditions to show that twisted unitary t-groups automatically correspond to quantum codes with distance d = t + 1. Moreover, these methods produce …
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On hochschild cohomology and modular representation theory
… is to study local and global invariants in representation theory of finite groups using the (restricted) Lie algebra structure of the first degree of Hochschild cohomology of a block algebra B as a main tool. This lead to two directions: In the first part we investigate the global approach. …
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Distributivity and quantification in discourse representation theory
In this study, I designed a system of NP semantics in the frame work of DRT by adopting the following assumptions: (i) Every indefinite NP is translated into a variable. (ii) The determiner quantifier of an NP does not provide quantificational force, but is an indicator of how many atomic …
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Q-systems and generalizations in representation theory
We study tau-functions given as matrix elements for the action of loop groups, $\widehat{GL_n}$ on $n$-component fermionic Fock space. In the simplest case, $n=2$, the tau-functions are equal to Hankel determinants and applying the famous Desnanot-Jacobi identity, one can see that they satisfy a …
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Representation theory of the global Cherednik algebra
This thesis studies the representation theory of Cherednik algebras associated to a complex algebraic varieties which carries the action of a finite group. First, we prove that the Knizhnik-Zamolodchikov functor from the category of P-coherent modules for the Cherednik algebra to finite dimensional …
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Representation Theory of Orders over Cohen-Macaulay Rings
… of the thesis focuses on various aspects of the representation theory of orders.</p> <p>We investigate orders which have finite global dimension on the punctured spectrum, but</p> <p>are not necessarily isolated singularities. In this case we are able to prove a generalization</p> <p>of …
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The Modern Representation Theory of the Symmetric Groups
… to inductively parametrizing all irreducible representations of the symmetric groups. This theory is then used to answer questions concerning to central projections in the group algebra. We index units first by partitions, and then by so called standard tableaux. We also present a new result …
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Power operations and central maps in representation theory
… Steenrod's operations and Smith's localization theory) to representation theory (especially in the context of the geometric Satake equivalence). In Chapter 2, we use Steenrod's construction to prove that the quantum Coulomb branch is a Frobenius-constant quantization. We also demonstrate the …
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Representation theory, Borel cross-sections, and minimal measures
… are in one-to-one correspondence with the representations of the form Γ:C<sub>b</sub>(E) → L<sup>∞</sup>(μ) with Γ(f∘Π) = f for every f ∈ C<sub>b</sub>(X). The representations are also in one-to-one correspondence with equivalence classes of the minimal measures on E. Now let E, X, and μ be …
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Representation theory of algebras related to the partition algebra
… this thesis is to determine the complex generic representation theory of the Juyumaya algebra. We do this by showing that a certain specialization of this algebra is isomorphic to the small ramified partition algebra, introduced by Martin (the representation theory of which is computable by a …
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The analysis of symmetric structures using group representation theory.
Group Representation Theory is the mathematical language best suited to describing the symmetry properties of a structure, and a structural analysis can utilises Group Representation Theory to provide the most efficient and systematic method of exploiting the full symmetry properties of any …
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The geometry and representation theory of superconformal quantum mechanics
… arising in the DLCQ of the six-dimensional (2,0) theory and four-dimensional $\mathcal{N}=4$ SUSY Yang-Mills. In the (2,0) case we carry out a detailed study of the representation theory of the light-cone superalgebra $\mathfrak{osp}(4^*|4)$. We give a complete classification of the unitary …
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On Problems in the Representation Theory of Symmetric Groups
In this thesis, we study the representation theory of the symmetric groups $\mathfrak{S}_n$, their Sylow $p$-subgroups $P_n$ and related algebras. For all primes $p$ and natural numbers $n$, we determine the maximum number of distinct irreducible constituents of degree coprime to $p$ of …
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