scholarly journals A global view of equivariant vector bundles and Dirac operators on some compact homogeneous spaces

2008 ◽  
pp. 399-415 ◽  
Author(s):  
Marc A. Rieffel
Keyword(s):  
Vector Bundles ◽  
Homogeneous Spaces ◽  
Dirac Operators ◽  
Global View

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 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.

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.

Vector bundles and homogeneous spaces

2010 ◽  
pp. 196-222 ◽  
Author(s):  
M. F. Atiyah ◽  
F. Hirzebruch ◽  
J. F. Adams
Keyword(s):  
Vector Bundles ◽  
Homogeneous Spaces
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