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Description: |
In this talk, we introduce a matroid invariant known as the rank partition which was defined by J. A. Dias da Silva in 1990. For matroids realizable over the complex numbers, following recent work of A. Berget, we explain how this concept relates matroid theory to the representation theory of the complex general linear group GLm(C).
In addition, we present an elegant duality, usually referred to as Schur-Weyl duality, between the representations of GLm(C) and those of an algebraic structure called the rook monoid.
The rook monoid is an extension of the symmetric group and thus its representation theory provides a natural context to generalize concepts such as symmetry classes of tensors and symmetrized tensors. We present such generalizations and how they may be applied to obtain new results in matroid theory involving the rank partition.
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Date: |
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| Start Time: |
15:00 |
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Speaker: |
Inês Legatheaux Martins (CELC, Univ. Lisboa)
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Institution: |
Faculdade de Ciências da Universidade de Lisboa, Centro de Estruturas Lineares e Combinatórias
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Place: |
Room 5.5 (DMUC)
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| Research Groups: |
-Algebra and Combinatorics
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See more:
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<Main>
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