GEOMETRY OF QUANTUM HOMOGENEOUS VECTOR BUNDLES AND REPRESENTATION THEORY OF QUANTUM GROUPS I

1999 ◽  
Vol 11 (05) ◽  
pp. 533-552 ◽  
Author(s):  
A. R. GOVER ◽  
R. B. ZHANG
Keyword(s):  
Representation Theory ◽  
Finite Type ◽  
Quantum Groups ◽  
Vector Bundles ◽  
Homogeneous Spaces ◽  
Projective Modules ◽  
Geometrical Structures ◽  
Induced Representations ◽  
Compact Quantum Groups ◽  
Homogeneous Vector

Quantum homogeneous vector bundles are introduced in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies, and their sections furnish finite type projective modules over algebras of functions on quantum homogeneous spaces. Further properties of the quantum homogeneous vector bundles are investigated, and applied to the study of the geometrical structures of induced representations of quantum groups.

scholarly journals Homogeneous vector bundles on homogeneous spaces

Topology ◽  
1972 ◽  
Vol 11 (2) ◽  
pp. 199-203 ◽  
Author(s):  
Harsh V. Pittie
Keyword(s):  
Vector Bundles ◽  
Homogeneous Spaces ◽  
Homogeneous Vector

scholarly journals EMBEDDING ERGODIC ACTIONS OF COMPACT QUANTUM GROUPS ON C*-ALGEBRAS INTO QUOTIENT SPACES

2007 ◽  
Vol 18 (02) ◽  
pp. 137-164 ◽  
Author(s):  
CLAUDIA PINZARI
Keyword(s):  
Quantum Groups ◽  
Reciprocity Theorem ◽  
Sufficient Condition ◽  
Alternative Definition ◽  
Topological Transitivity ◽  
Frobenius Reciprocity ◽  
Induced Representations ◽  
C Algebras ◽  
Quotient Spaces ◽  
Compact Quantum Groups

The notion of compact quantum subgroup is revisited and an alternative definition is given. Induced representations are considered and a Frobenius reciprocity theorem is obtained. A relationship between ergodic actions of compact quantum groups on C*-algebras and topological transitivity is investigated. A sufficient condition for embedding such actions in quantum quotient spaces is obtained.

scholarly journals FROM COMPLETE TO PARTIAL FLAGS IN GEOMETRIC EXTENSION ALGEBRAS

2017 ◽  
Vol 60 (1) ◽  
pp. 111-121
Author(s):  
JULIA SAUTER
Keyword(s):  
Vector Bundles ◽  
Homogeneous Spaces ◽  
Locally Finite ◽  
Perverse Sheaf ◽  
Constant Sheaf ◽  
Push Forward ◽  
Complete Flag ◽  
Extension Algebra ◽  
The Relationship ◽  
Homogeneous Vector

AbstractA geometric extension algebra is an extension algebra of a semi-simple perverse sheaf (allowing shifts), e.g., a push-forward of the constant sheaf under a projective map. Particular nice situations arise for collapsings of homogeneous vector bundles over homogeneous spaces. In this paper, we study the relationship between partial flag and complete flag cases. Our main result is that the locally finite modules over the geometric extension algebras are related by a recollement. As examples, we investigate parabolic affine nil Hecke algebras, geometric extension algebras associated with parabolic Springer maps and an example of Reineke of a parabolic quiver-graded Hecke algebra.

scholarly journals An invariant for homogeneous spaces of compact quantum groups

2016 ◽  
Vol 301 ◽  
pp. 258-288 ◽  
Author(s):  
Partha Sarathi Chakraborty ◽  
Arup Kumar Pal
Keyword(s):  
Quantum Groups ◽  
Homogeneous Spaces ◽  
Compact Quantum Groups

scholarly journals Induction for locally compact quantum groups revisited

2019 ◽  
Vol 150 (2) ◽  
pp. 1071-1093
Author(s):  
Mehrdad Kalantar ◽  
Paweł Kasprzak ◽  
Adam Skalski ◽  
Piotr M. Sołtan
Keyword(s):  
Quantum Groups ◽  
General Setting ◽  
Locally Compact ◽  
Induced Representations ◽  
Open Quantum ◽  
Locally Compact Quantum Groups ◽  
Weak Containment ◽  
Compact Quantum Groups

AbstractIn this paper, we revisit the theory of induced representations in the setting of locally compact quantum groups. In the case of induction from open quantum subgroups, we show that constructions of Kustermans and Vaes are equivalent to the classical, and much simpler, construction of Rieffel. We also prove in general setting the continuity of induction in the sense of Vaes with respect to weak containment.

SELECTED TOPICS IN QUANTUM GROUPS

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 859-887 ◽  
Author(s):  
YAN S. SOIBELMAN
Keyword(s):  
Representation Theory ◽  
Quantum Groups ◽  
Compact Quantum Groups

Some recent results in the representation theory of the algebras of functions on compact quantum groups are presented. Applications to different subjects are given.

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