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On the representation theory of braid groups

Ivan Marin (2013)

Annales mathématiques Blaise Pascal

This work presents an approach towards the representation theory of the braid groups $B_{n}$ . We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids, with the help of Drinfeld associators. We set a dictionary between representation-theoretic properties of these two structures, and tools to describe the representations thus obtained. We give an explanation for the frequent apparition of unitary structures on classical...

Plane curves associated to character varieties of 3-manifolds.

M. Culler, H. Gillet, D. Cooper (1994)

Inventiones mathematicae

Quadratische Formen in additiven Kategorien

Heinz-Georg Quebbemann, Rudolf Scharlau, Winfried Scharlau, M. Schulte (1976)

Mémoires de la Société Mathématique de France

Quotients infinitésimaux du groupe de tresses

Ivan Marin (2003)

Annales de l’institut Fourier

Nous définissons et entamons l’étude d’analogues infinitésimaux des quotients principaux (algèbres de Temperley-Lieb, Hecke, Birman-Wenzl-Murakami) de l’algèbre de groupe du groupe d’Artin $B_{n}$ . Ce sont des algèbres de Hopf qui correspondent à des groupes réductifs, et permettent de donner un cadre général aux représentations dérivées des représentations classiques de $B_{n}$ . Nous décomposons complètement l’algèbre de Temperley-Lieb infinitésimale, et en déduisons plusieurs résultats d’irréductibilité.

Radicals of semi-group rings

Jan Krempa (1974)

Fundamenta Mathematicae

Rational Functions Invariant under a Finite Abelian Group.

H.W. Jr. Lenstra (1974)

Inventiones mathematicae

Remarks on Characters of Discrete Nilpotent Groups.

Ernest Plonka (1979)

Mathematische Annalen

Representations in SU(2) of the fundamental groups of the Whitehead link and of doubled knots.

Eric P. Klassen (1993)

Forum mathematicum

Representations of group and semigroup actions

Walter S. Sizer (1984)

Czechoslovak Mathematical Journal

Representations of infinite weak product groups

Donald Bures (1970)

Compositio Mathematica

...-Ringstrukturen auf dem Burnsidering der Permutationsdarstellungen einer endlichen Gruppe.

Christian Siebeneicher (1976)

Mathematische Zeitschrift

R-S correspondence for $(ℤ_{2} \times ℤ_{2}) ≀ S_{n}$ and Klein-4 diagram algebras.

Parvathi, M., Sivakumar, B. (2008)

The Electronic Journal of Combinatorics [electronic only]

Skew-representations of a group by transformations on its subgroups

Liu, Tsai-Sheng (1974)

Portugaliae mathematica

SO3 (...)-representation curves for two-bridge knot groups.

Michael Heusener (1994)

Mathematische Annalen

Some Generalized Characters of Finite Chevalley Groups.

John W. Ballard (1976)

Mathematische Zeitschrift

The Roquette category of finite $p$ -groups

Serge Bouc (2015)

Journal of the European Mathematical Society

Let $p$ be a prime number. This paper introduces the Roquette category $ℛ_{p}$ of finite $p$ -groups, which is an additive tensor category containing all finite $p$ -groups among its objects. In $ℛ_{p}$ , every finite $p$ -group $P$ admits a canonical direct summand $\partial P$ , called the edge of $P$ . Moreover $P$ splits uniquely as a direct sum of edges of Roquette $p$ -groups, and the tensor structure of $ℛ_{p}$ can be described in terms of such edges. The main motivation for considering this category is that the additive functors from $ℛ_{p}$ to...

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