Multi-valued representation
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
.
References
[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) |
Multi-valued representation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multi-valued_representation&oldid=47924