# GROBNER-SHIRSHOV BASES FOR REPRESENTATION THEORY

• Kang, Seok-Jin ;
• Lee, Kyu-Hwan
• Published : 2000.01.01
• 36 3

#### Abstract

In this paper, we develop the Grobner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Grobner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite dimensional irreducible representations of the simple tie algebra sl$_3$. Each of these monomial bases is in 1-1 correspondence with the set of semistandard Young tableaux with a given shape.

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