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1	The Stone-von Neumann Construction in Branching Rules and Minimal Degree Problems Karimianpour, Camelia January 2016 (has links) In Part I, we investigate the principal series representations of the n-fold covering groups of the special linear group over a p-adic field. Such representations are constructed via the Stone-von Neumann theorem. We have three interrelated results. We first compute the K-types of these representations. We then give a complete set of reducibility points for the unramified principal series representations. Among these are the unitary unramified principal series representations, for which we further investigate the distribution of the K-types among its irreducible components. In Part II, we demonstrate another application of the Stone-von Neumann theorem. Namely, we present a lower bound for the minimal degree of a faithful representation of an adjoint Chevalley group over a quotient ring of a non-Archimedean local field. Stone-von Neumann theorem p-adic field representation
2	Forma traço sobre algumas extensões galoisianas de corpos p-Ádicos Prado, Janete do [UNESP] 28 February 2005 (has links) (PDF) Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-02-28Bitstream added on 2014-06-13T20:08:01Z : No. of bitstreams: 1 prado_j_me_sjrp.pdf: 438115 bytes, checksum: 072493cefd49a6603f89810da896f173 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Seja K um corpo p-ádico, com p 6= 2 e F K uma extensão galoisiana de K de grau n: Então F pode ser visto como espa»co quadrático sobre K, com a forma quadrática dada por T(x) = trFjK(x2), para x 2 F: Determinaremos os invariantes determinante, dimensão e invariante de Hasse desta forma quadrática para n igual a 2,3 e 4. / Let K be a p-adic eld with p 6= 2 and F a Galois extension eld of K of degree n: Then F can be viewed as a quadratic space over K under the quadratic form T(x) = trFjK(x2) for x 2 F. The invariants of this quadratic form dimension, determinant and Hasse invariant are given in the case when n is equal to 2,3 and 4. Álgebra Invariantes Corpos locais (Algebra) Extensões de corpos (Matematica) Forma quadrática Forma traço Quadratic form Trace form Hasse invariant p-Adic field
3	Forma traço sobre algumas extensões galoisianas de corpos p-Ádicos / Prado, Janete do. January 2005 (has links) Orientador: Clotilzio Moreira dos Santos / Banca: Ires Dias / Banca: Aparecida Francisco da Silva / Resumo: Seja K um corpo p-ádico, com p 6= 2 e F K uma extensão galoisiana de K de grau n: Então F pode ser visto como espa»co quadrático sobre K, com a forma quadrática dada por T(x) = trFjK(x2), para x 2 F: Determinaremos os invariantes determinante, dimensão e invariante de Hasse desta forma quadrática para n igual a 2,3 e 4. / Let K be a p-adic eld with p 6= 2 and F a Galois extension eld of K of degree n: Then F can be viewed as a quadratic space over K under the quadratic form T(x) = trFjK(x2) for x 2 F. The invariants of this quadratic form dimension, determinant and Hasse invariant are given in the case when n is equal to 2,3 and 4. / Mestre Álgebra. Invariantes. Corpos locais (Algebra) Extensões de corpos (Matematica) Quadratic form. eng Trace form. eng Hasse invariant. eng p-Adic field. eng
4	Produits tensoriels en théorie de Hodge p-adique / Tensor products in p-adic Hodge theory Di Matteo, Giovanni 12 December 2013 (has links) Soient K/Qp une extension finie et GK le groupe de Galois absolu de K. Cette thèse est consacrée à l'étude de produits tensoriels cristallins (ou semi-stables, ou de de Rham, ou de Hodge-Tate) de représentations p-adiques de GK,, ainsi que de produits tensoriels triangulins de représentations p-adiques de GK. On étudie également la situation où l'image d'une représentation p-adique par un foncteur de Schur (tel Symn ou Λn) est cristalline (ou semi-stable, ou de de Rham, ou de Hodge-Tate). Les résultats présentés dans cette thèse sont énoncés pour les B-paires, et ils s'appliquent donc en particulier aux représentations p-adiques. / Let K/Qp be a finite extension and let GK be the absolute Galois group of K. This thesis is devoted to the study of crystalline (as well as semi-stable, de Rham, or Hodge-Tate) tensor products of p-adic representations of GK, as well as trianguline tensor products of p-adic representations of p-adic representations of GK. We also study the situation when the image of a p-adic representation by a Schur functor (for example, Symn or Λn) is crystalline (or semi-stable, or de Rham, or Hodge-Tate). The results presented in this thesis are stated for B-pairs, and apply in particular to p-adic representations. B-paire Théorie de Hodge p-adique Représentation cristalline Représentation semi-stable Représentation de de Rham Représentation de Hodge-Tate Représentation trianguline Produit tensoriel Foncteur de Schur B-pairs P-adic Hodge theory Crystalline representation Semi-stable representation De Rham representation Hodge-Tate representation Trianguline representation Tensor product Schur functor 510

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