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Displaying similar documents to “Reciprocity theorems in the theory of representations of groups and algebras”

Factor representations of diffeomorphism groups

Robert P. Boyer (2003)

Studia Mathematica

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We give a new construction of semifinite factor representations of the diffeomorphism group of euclidean space. These representations are in canonical correspondence with the finite factor representations of the inductive limit unitary group. Hence, many of these representations are given in terms of quasi-free representations of the canonical commutation and anti-commutation relations. To establish this correspondence requires a generalization of complete positivity as developed in...

Representations of the direct product of matrix algebras

Daniele Guido, Lars Tuset (2001)

Fundamenta Mathematicae

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Suppose B is a unital algebra which is an algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the σ-complete ultrafilters on X (Theorem 2.6). Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducible representations of B are labeled by points of X, and all representations of B are described (Theorem...

On the representation theory of braid groups

Ivan Marin (2013)

Annales mathématiques Blaise Pascal

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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...