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Lie algebras and classical partition identities.
1Department of Mathematics, Yale University, New Haven, Connecticut 06520.
Summary
This study reinterprets Macdonald
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.