Geometric Representation Theory and Extended Affine Lie Algebras

2011 ◽  
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Geometric Representation ◽  
Affine Lie Algebras ◽  
Geometric Representation Theory

Borel subalgebras of restricted Cartan-Type Lie algebras

2021 ◽  
pp. 2250210
Author(s):  
Ke Ou ◽  
Bin Shu
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Open Problem ◽  
Conjugacy Classes ◽  
Classical Type ◽  
Geometric Representation ◽  
Cartan Type ◽  
Geometric Representation Theory ◽  
Geometric Setting

It is still an open problem to determine the conjugacy classes of Borel subalgebras of non-classical type Lie algebras. In this paper, we prove that there are at least 2 conjugacy classes of Borel subalgebras as well as maximal triangulable subalgebras of restricted Cartan type Lie algebras of type W, S and H. We are particularly interested in maximal triangulable subalgebras of [Formula: see text] under some conditions which is called [Formula: see text]-subalgebras (Definition 3.1). We classify the conjugacy classes of [Formula: see text]-subalgebras for [Formula: see text] and determine their representatives. This paper and its sequel [Z. Lin, K. Ou and B. Shu, Geometric Setting of Jacobson–Witt Algebras, preprint] attempt to establish both algebraic and geometric setting for geometric representation theory of [Formula: see text]

scholarly journals Geometric representation theory of restricted Lie algebras

2001 ◽  
Vol 6 (2) ◽  
pp. 175-191 ◽  
Author(s):  
I. Mirković ◽  
D. Rumynin
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Geometric Representation ◽  
Geometric Representation Theory ◽  
Restricted Lie Algebras

Enveloping Algebras and Geometric Representation Theory

2015 ◽  
Vol 12 (2) ◽  
pp. 1385-1447 ◽  
Author(s):  
Iain Gordon ◽  
Bernard Leclerc ◽  
Wolfgang Soergel
Keyword(s):  
Representation Theory ◽  
Geometric Representation ◽  
Enveloping Algebras ◽  
Geometric Representation Theory

scholarly journals Mixed motives and geometric representation theory in equal characteristic

2019 ◽  
Vol 25 (2) ◽  
Author(s):  
Jens Niklas Eberhardt ◽  
Shane Kelly
Keyword(s):  
Representation Theory ◽  
Geometric Representation ◽  
Geometric Representation Theory ◽  
Mixed Motives

An Application of U(g)-bimodules to Representation Theory of Affine Lie Algebras

2004 ◽  
Vol 7 (4) ◽  
pp. 457-469 ◽  
Author(s):  
Dražen Adamović
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Affine Lie Algebras

Representations of affine Lie algebras and soliton equations

1985 ◽  
Vol 315 (1533) ◽  
pp. 391-391
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Gordon Equation ◽  
Vries Equation ◽  
Affine Lie Algebras ◽  
Loop Groups ◽  
Sine Gordon Equation ◽  
Kyoto School ◽  
Hidden Symmetries ◽  
Soliton Equations

A few years ago the 'hidden symmetries’ of the soliton equations had been identified as affine Lie groups, also known as loop groups. The first extensive use of the representation theory of affine Lie algebras for the soliton equations have been developed in a series of works by mathematicians of the Kyoto school. We will review some of their results and develop them further on the basis of the representation theory. Thus an orbit of the simplest affine Lie group SL(2, C)^ in the fundamental representation V will provide the solutions of the Korteweg-de Vries equation, and similarly the solutions of the sine-Gordon equation will come from an orbit of the group (SL(2, C) x SL(2, C)) ^ in V x V*.

Geometric Representation Theory and Gauge Theory

2019 ◽  
Author(s):  
Alexander Braverman ◽  
Michael Finkelberg ◽  
Andrei Negut ◽  
Alexei Oblomkov
Keyword(s):  
Gauge Theory ◽  
Representation Theory ◽  
Geometric Representation ◽  
Geometric Representation Theory
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