### Generating functions for the Hochschild cohomology of symmetric groups

Algebra Seminar

1st March 2023, 2:30 pm – 3:30 pm

Fry Building, 2.04

We start out by reviewing some classical material on the representation

theory of symmetric groups and the Hochschild cohomology of

finite-dimensional algebras. We describe generating functions for the

dimensions of the Hochschild cohomology of symmetric groups in each degree.

While it is known, using the classification of finite simple groups, that

the first Hochschild cohomology of a non-semisimple finite group algebra is

non-zero, it remains an open question whether this is true for non-simple

blocks of finite groups. We use generating functions to show that the first

Hochschild cohomology of any non-simple block of a symmetric group algebra

is non-zero. This is joint work with Dave Benson and Radha Kessar.

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