W-algebra representation theory

2019 ◽  
Author(s):  
Aiden Suter
Keyword(s):  
Representation Theory ◽  
Algebra Representation

scholarly journals ON MULTI-COLOR PARTITIONS AND THE GENERALIZED ROGERS–RAMANUJAN IDENTITIES

2001 ◽  
Vol 03 (04) ◽  
pp. 533-548 ◽  
Author(s):  
NAIHUAN JING ◽  
KAILASH C. MISRA ◽  
CARLA D. SAVAGE
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Mathematical Physics ◽  
Infinite Dimensional ◽  
Algebra Representation ◽  
The Sixties ◽  
Lie Algebra Representation ◽  
New Interpretation

Basil Gordon, in the sixties, and George Andrews, in the seventies, generalized the Rogers–Ramanujan identities to higher moduli. These identities arise in many areas of mathematics and mathematical physics. One of these areas is representation theory of infinite dimensional Lie algebras, where various known interpretations of these identities have led to interesting applications. Motivated by their connections with Lie algebra representation theory, we give a new interpretation of a sum related to generalized Rogers–Ramanujan identities in terms of multi-color partitions.

WB algebra representation theory

1990 ◽  
Vol 339 (1) ◽  
pp. 177-190 ◽  
Author(s):  
G.M.T. Watts
Keyword(s):  
Representation Theory ◽  
Algebra Representation

scholarly journals On Representations of sl(n, C) Compatible with a Z2-grading

10.14311/1261 ◽  
2010 ◽  
Vol 50 (5) ◽  
Author(s):  
M. Havlíček ◽  
E. Pelantová ◽  
J. Tolar
Keyword(s):  
Irreducible Representation ◽  
Representation Theory ◽  
Lie Algebra ◽  
Finite Dimensional ◽  
Algebra Representation ◽  
Lie Algebra Representation ◽  
Generally True

This paper extends existing Lie algebra representation theory related to Lie algebra gradings. The notion of a representation compatible with a given grading is applied to finite-dimensional representations of sl(n,C) in relation to its Z2-gradings. For representation theory of sl(n,C) the Gel’fand-Tseitlin method turned out very efficient. We show that it is not generally true that every irreducible representation can be compatibly graded.

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