Geometric Methods in Representation Theory

1983 ◽  
pp. 283-290 ◽  
Author(s):  
Gregg J. Zuckerman
Keyword(s):  
Representation Theory ◽  
Geometric Methods

scholarly journals THE MONOID OF FAMILIES OF QUIVER REPRESENTATIONS

2002 ◽  
Vol 84 (3) ◽  
pp. 663-685 ◽  
Author(s):  
MARCUS REINEKE
Keyword(s):  
Algebraic Geometry ◽  
Group Theory ◽  
Representation Theory ◽  
Quantum Group ◽  
Subject Classification ◽  
Quiver Representations ◽  
Enveloping Algebras ◽  
Geometric Methods ◽  
Quantized Enveloping Algebras ◽  
Monoid Structure

A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, that is, subvarieties of the varieties of representations. The study of this monoid leads to interesting interactions between representation theory, algebraic geometry and quantum group theory. For example, it produces a wealth of interesting examples of families of quiver representations, which can be analysed by representation-theoretic and geometric methods. Conversely, results from representation theory, in particular A. Schofield's work on general properties of quiver representations, allow us to relate the monoid to certain degenerate forms of quantized enveloping algebras.2000 Mathematical Subject Classification: 16G20, 14L30, 17B37.

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products
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