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A Centraliser Analogue to the Farahat-Higman Algebra by Creedon, Samuel is a scholarly article available to read on EtoBox.

What is A Centraliser Analogue to the Farahat-Higman Algebra about?

We define a family of algebras \mathsf{FH}_{m} which generalise the Farahat-Higman algebra introduced in [FH59] by replacing the role of the center of the group algebra of the symmetric groups with centraliser algebras of symmetric groups. These algebras have a basis indexed by marked cycle shapes, combinatorial objects which generalise proper integer partitions. We analyse properties of marked cycle shapes and of the algebras \mathsf{FH}_{m}, demonstrating that some of the former govern the latter. The main theorem of the paper proves that the algebra \mathsf{FH}_{m} is isomorphic to the tensor product of the degenerate affine Hecke algebra with the algebra of symmetric functions.

Author

Creedon, Samuel

Published

2022

Language

EN