Multi-valued representation

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of a connected topological group

An ordinary representation of a connected topological group (cf. Representation of a topological group) such that is isomorphic (as a topological group) to a quotient group of relative to a discrete normal subgroup which is not contained in the kernel of . A multi-valued representation is called -valued if contains exactly elements. By identifying the elements of with the elements of one obtains for the sets , , the relations , , . Multi-valued representations of connected, locally path-connected topological groups exist only for non-simply-connected groups. The most important example of a multi-valued representation is the spinor representation of the complex orthogonal group , ; this representation is a two-valued representation of and is determined by a faithful representation of the universal covering group of .


[1] A.A. Kirillov, "Elements of the theory of representations" , Springer (1976) (Translated from Russian)
[2] M.A. Naimark, "Theory of group representations" , Springer (1982) (Translated from Russian)
How to Cite This Entry:
Multi-valued representation. A.I. Shtern (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098