Semisimplicity and Tensor Products of Group Representations: Converse Theorems

2000 ◽  
pp. 571-595
Author(s):  
Jean-Pierre Serre
Keyword(s):  
Tensor Products ◽  
Group Representations ◽  
Converse Theorems

scholarly journals Semisimplicity and Tensor Products of Group Representations: Converse Theorems

1997 ◽  
Vol 194 (2) ◽  
pp. 496-520 ◽  
Author(s):  
Jean-Pierre Serre ◽  
Walter Feit
Keyword(s):  
Tensor Products ◽  
Group Representations ◽  
Converse Theorems

scholarly journals A Stone-Weierstrass theorem for group representations

1978 ◽  
Vol 1 (2) ◽  
pp. 235-244 ◽  
Author(s):  
Joe Repka
Keyword(s):  
Compact Group ◽  
Unitary Representation ◽  
Regular Representation ◽  
Discrete Series ◽  
Series Representation ◽  
Tensor Products ◽  
Weil Representation ◽  
Weierstrass Theorem ◽  
Group Representations ◽  
Discrete Series Representation

It is well known that ifGis a compact group andπa faithful (unitary) representation, then each irreducible representation ofGoccurs in the tensor product of some number of copies ofπand its contragredient. We generalize this result to a separable typeIlocally compact groupGas follows: letπbe a faithful unitary representation whose matrix coefficient functions vanish at infinity and satisfy an appropriate integrabillty condition. Then, up to isomorphism, the regular representation ofGis contained in the direct sum of all tensor products of finitely many copies ofπand its contragredient.We apply this result to a symplectic group and the Weil representation associated to a quadratic form. As the tensor products of such a representation are also Weil representations (associated to different forms), we see that any discrete series representation can be realized as a subrepresentation of a Weil representation.

scholarly journals QUANTUM GROUP-TWISTED TENSOR PRODUCTS OF C*-ALGEBRAS

2014 ◽  
Vol 25 (02) ◽  
pp. 1450019 ◽  
Author(s):  
RALF MEYER ◽  
SUTANU ROY ◽  
STANISŁAW LECH WORONOWICZ
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Quantum Group ◽  
Quantum Groups ◽  
Tensor Products ◽  
Group Representations ◽  
Basic Properties ◽  
C Algebras ◽  
Twisted Tensor Product

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways, based on certain pairs of quantum group representations and based on covariant Hilbert space representations, respectively. We establish basic properties of the twisted tensor product and study some examples.

scholarly journals Braid Group Representations from Twisted Tensor Products of Algebras

2020 ◽  
Vol 3 (2) ◽  
pp. 103-130 ◽  
Author(s):  
Paul Gustafson ◽  
Andrew Kimball ◽  
Eric C. Rowell ◽  
Qing Zhang
Keyword(s):  
Braid Group ◽  
Tensor Products ◽  
Group Representations

HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND TENSOR PRODUCTS OF SYMMETRIC GROUP REPRESENTATIONS

1991 ◽  
Vol 01 (02) ◽  
pp. 207-221 ◽  
Author(s):  
JEAN-YVES THIBON
Keyword(s):  
Hopf Algebra ◽  
Tensor Product ◽  
Symmetric Group ◽  
Hopf Algebras ◽  
Symmetric Functions ◽  
Tensor Products ◽  
Ring Structure ◽  
Algebra Structure ◽  
Group Representations ◽  
Symmetric Group Representations

The Hopf algebra structure of the ring of symmetric functions is used to prove a new identity for the internal product, i.e., the operation corresponding to the tensor product of symmetric group representations. From this identity, or by similar techniques which can also involve the λ-ring structure, we derive easy proofs of most known results about this operation. Some of these results are generalized.

Weak containment and tensor products of group representations

1982 ◽  
Vol 180 (1) ◽  
pp. 107-117 ◽  
Author(s):  
Eberhard Kaniuth
Keyword(s):  
Tensor Products ◽  
Group Representations ◽  
Weak Containment
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