Representation Theory of The $W_{1+\infty}$ Algebra
H.Awata, M.Fukuma, Y.Matsuo, S.Odake
TL;DR
This paper reviews recent advances in the representation theory of the $W_{1+ abla}$ algebra, covering topics like quasifinite representations, free field realizations, and subalgebra structures, highlighting new developments in mathematical physics.
Contribution
It provides a comprehensive overview of recent progress in understanding the structure and representations of the $W_{1+ abla}$ algebra, including new results on subalgebras and character formulas.
Findings
Analysis of quasifinite representations
Development of free field realizations
Structure of subalgebras like $W_ abla$
Abstract
We review the recent development in the representation theory of the algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (Super) Matrix Generalization, Structure of subalgebras such as algebra, Determinant formula, Character formula. (Invited talk at ``Quantum Field Theory, Integrable Models and Beyond", YITP, 14-17 February 1994. To appear in Progress of Theoretical Physics Proceedings Supplement.)
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Algebraic structures and combinatorial models