On the representation theory of partial Brauer algebras

By Paul P. Martin, Volodymyr Mazorchuk. 2012

49 citations recorded by the source corpus.

In this paper we study the partial Brauer $\mathbb{C}$-algebras $\mathfrak{R}_n(\delta,\delta')$, where $n \in \mathbb{N}$ and $\delta,\delta'\in\mathbb{C}$. We show that these algebras are generically semisimple, construct the Specht modules and determine the Specht module restriction rules for the restriction $\mathfrak{R}_{n-1} \hookrightarrow \mathfrak{R}_n$. We also determine the corresponding decomposition matrix, and the Cartan decomposition matrix.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1942c7fb75f3acd0a2522109d7533edfe8ce8a85

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In Algebra and Number Theory

1. Elise delMas
2. Tom Halverson

In Geometry and Topology

1. Elise delMas
2. Tom Halverson
3. Rosa C. Orellana
4. Mike Zabrocki

In Statistical and Nonlinear Physics

1. Tom Halverson
2. Elise delMas

Citations in the corpus

• Representations of the Rook-Brauer Algebra (2012, methodology): “Representations of the rook-Brauer algebra are studied independently (and simultaneously with this work) by Martin and Mazorchuk [MM] using different methods.”