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 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

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 Fano 3-folds from homogeneous vector bundles over Grassmannians

2021 ◽  
Author(s):  
Lorenzo De Biase ◽  
Enrico Fatighenti ◽  
Fabio Tanturri
Keyword(s):  
Vector Bundles ◽  
Homogeneous Vector

AbstractWe rework the Mori–Mukai classification of Fano 3-folds, by describing each of the 105 families via biregular models as zero loci of general global sections of homogeneous vector bundles over products of Grassmannians.

scholarly journals UNARY FA-PRESENTABLE SEMIGROUPS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250038 ◽  
Author(s):  
ALAN J. CAIN ◽  
NIK RUŠKUC ◽  
RICHARD M. THOMAS
Keyword(s):  
Difficult Problem ◽  
Decision Problems ◽  
Finite Model ◽  
Locally Finite ◽  
Letter Alphabet ◽  
Significant Interest ◽  
Automatic Presentations ◽  
The Relationship ◽  
Completely Simple

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classification of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a difficult problem in general. A restricted problem, also of significant interest, is to ask this question for unary automatic presentations: automatic presentations over a one-letter alphabet. This paper studies unary FA-presentable semigroups. We prove the following: Every unary FA-presentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a one-letter alphabet. Unary FA-presentable semigroups are locally finite, but non-finitely generated unary FA-presentable semigroups may be infinite. Every unary FA-presentable semigroup satisfies some Burnside identity. We describe the Green's relations in unary FA-presentable semigroups. We investigate the relationship between the class of unary FA-presentable semigroups and various semigroup constructions. A classification is given of the unary FA-presentable completely simple semigroups.

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