Representation-theoretic derivation of the Temperley-Lieb-Martin algebras
Tomasz Brzezinski, Jacob Katriel
TL;DR
This paper derives explicit algebraic expressions for Temperley-Lieb-Martin algebras using Hecke algebra representation theory, focusing on restrictions based on Young diagram shapes, and extends techniques to related algebraic structures.
Contribution
It provides a representation-theoretic derivation of Temperley-Lieb-Martin algebras and constructs related algebras with specific Young diagram restrictions.
Findings
Explicit formulas for Temperley-Lieb-Martin algebras derived
Construction of algebras with restrictions on Young diagram shapes
Use of Hecke algebra representation theory in algebra derivation
Abstract
Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the quotients of the Hecke algebra that admit only representations corresponding to Young diagrams with a given maximum number of columns (or rows), are obtained, making explicit use of the Hecke algebra representation theory. Similar techniques are used to construct the algebras whose representations do not contain rectangular subdiagrams of a given size.
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