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Lie algebras and classical partition identities.

J Lepowsky¹, S Milne

¹Department of Mathematics, Yale University, New Haven, Connecticut 06520.

Proceedings of the National Academy of Sciences of the United States of America

|February 1, 1978

Summary

This study reinterprets Macdonald

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Area of Science:

Combinatorics
Representation Theory
Algebraic Combinatorics

Background:

Macdonald's unspecialized identities are fundamental in combinatorics.
The Rogers-Ramanujan identities are a classic result in partition theory.
The Weyl-Kac character formula connects representation theory and Lie algebras.

Purpose of the Study:

To interpret Macdonald's unspecialized identities as multivariable vector partition theorems.
To establish a connection between these identities and the Weyl-Kac character formula.

Main Methods:

Interpreting identities within the framework of vector partitions.
Applying techniques from representation theory of Lie algebras.

Main Results:

Macdonald's unspecialized identities are shown to be multivariable vector partition theorems.
A novel relationship is established between partition identities and the Weyl-Kac character formula for a specific class of Lie algebras.

Conclusions:

This work provides a new perspective on Macdonald's identities.
The findings bridge concepts in partition theory and infinite-dimensional Lie algebra representation theory.

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