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Showing 1 to 20 of 31 for “"Irreducible Representations"”.
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The Irreducible Representations of D2n
<p>Irreducible representations of a finite group over a field are important because all representations of a group are direct sums of irreducible representations. Maschke tells us that if φ is a representation of the finite group G of order n on the m-dimensional space V over the field K of complex …
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Irreducible Representations from Group Actions on Trees
<p>We study the representations of the symmetric group $S_n$ found by acting on</p> <p>labeled graphs and trees with $n$ vertices. Our main results provide</p> <p>combinatorial interpretations that give the number of times the irreducible</p> <p>representations associated with the integer …
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Irreducible representations of braid groups via quantized enveloping algebras
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.
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C*-algebras of the planar crystal groups and their irreducible *-representations
… result is the explicit description of all the irreducible *-representations of these C*-Algebras. Two further applications are described in the concluding paragraph below. The study of generalized representation theory arose from the study of unitary representations of groups. Quantum theory, …
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Representations of Cherednik algebras in positive characteristic
In this thesis, we first classify the irreducible representations of the rational Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. One is the "quantum" case, where "Planck's constant" is nonzero and generic irreducible representations have dimension pr, where r is the …
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Lifting Galois Representations in a Conjecture of Figueiredo
… on the correspondence between degree 2 odd irreducible representations of the absolute Galois group of Q and modular forms. Letting M be an imaginary quadratic field, L.M. Figueiredo gave a related conjecture concerning degree 2 irreducible representations of the absolute Galois group of M …
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On representations of quantum groups and Cherednik algebras
… . We calculate the characters of all irreducible representations in category 0 of the rational Cherednik algebra for W the exceptional Coxeter group H3 and for W the complex reflection group G12 . In particular, we determine which of the irreducible representations are …
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Metacyclic groups of odd order
… problem to that of determining all metacyclic irreducible linear groups over finite prime fields. The central topic of this thesis is a description of a theoretical approach to the problem for groups of odd order. The first part of the thesis is devoted to the determination of the abstract …
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Metacyclic groups of odd order
… problem to that of determining all metacyclic irreducible linear groups over finite prime fields. The central topic of this thesis is a description of a theoretical approach to the problem for groups of odd order. The first part of the thesis is devoted to the determination of the abstract …
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Higher Specht Polynomials for Representations of Iwahori-Hecke Algebras
… action of 𝑆_𝑛, and they will decompose 𝕮 into irreducible representations of the Hecke algebra. These irreducible representations are 𝑞-Specht modules 𝑆_λ^𝑞. In this construction, if we consider 𝑞 = 1 then we obtain the original higher Specht polynomials for 𝑆_𝑛. We will also introduce a …
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Rings of regular functions on spherical nilpotent orbits for complex classical groups
… In this thesis, we will decompose it into irreducible representations of G for some spherical nilpotent orbits.
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On representations of rational Cherednik algebras
… of finite groups of Lie type. In particular, irreducible representations in the rational Cherednik category O with particular generalized support conditions correspond to irreducible representations of associated generalized Hecke algebras. An explicit presentation for these generalized Hecke …
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The Modern Representation Theory of the Symmetric Groups
… A. Okounkov, 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 …
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Smooth ℓ-modular representations of unramified p -adic U(2, 1)(E/F)
… In this thesis we construct all ℓ-modular irreducible cuspidal representations of G by compact induction from irreducible representations of compact open subgroups of G. Under an assumption on the possible cuspidal subquotients of representations parabolically induced from an irreducible …
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Matrix Representations of Automorphism Groups of Free Groups
… theory of Aut (Fn). We also calculate irreducible representations of Aut (Fn) in low dimensions and for small n.
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Boundaries of K-types in discrete series
Abstract: A fundamental problem about irreducible representations of a reductive Lie group G is understanding their restriction to a maximal compact subgroup K. In certain important cases, known as the discrete series, we have a formula that gives the multiplicity of any given irreducible …
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The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups
… 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 representations. In this paper we present a generalized …
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Forcing in Analysis and Combinatorics
… with exactly two inequivalent irreducible representations. Such a $\textrm{C}^\ast$-algebra cannot satisfy the conclusion of Glimm's Dichotomy Theorem. (3) Studying families of infinite block sequences of elements of the space $\textrm{FIN}_k$, Ramsey properties of such …
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Cryo-electron microscopy image analysis using multi-frequency vector diffusion maps
… denoising. This framework incorporates different irreducible representations of the estimated alignment between similar images. In addition, we propose a graph filtering scheme to denoise the images using the eigenvalues and eigenvectors of the MFVDM matrices. Through both simulated and publicly …
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