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Showing 1 to 5 of 5 for “"Young diagrams"”.
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Root-theoretic Young diagrams and Schubert Calculus
… problems from the common lens of root-theoretic Young diagrams (RYDs). In terms of RYDs, we present nonnegative Schubert calculus rules for the (co)adjoint varieties of classical Lie type. Using these we give polytopal descriptions of the set of nonzero Schubert structure constants for the …
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Specht modules and Schubert varieties for general diagrams
… all of which are indexed by partitions and their Young diagrams. We will generalize these objects to allow for not just Young diagrams but arbitrary collections of boxes or, equally well, bipartite graphs. We will then provide evidence for a conjecture that the relation between the areas described …
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Matrix Representations of Automorphism Groups of Free Groups
… subgroups is well understood in the language of Young Diagrams, and we apply this knowledge to better understand the representation theory of Aut (Fn). We also calculate irreducible representations of Aut (Fn) in low dimensions and for small n.
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Counting coloured boxes
… generating functions for three-dimensional Young diagrams (also called plane partitions). The variables correspond to a colouring of the boxes according to a finite abelian subgroup G of SO(3). These generating functions turn out to be orbifold Donaldson-Thomas partition functions for the …
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The Modern Representation Theory of the Symmetric Groups
The goal of this thesis is to first give an overview of the modern approach, using the paper of A. Vershik and A. Okounkov, to inductively parametrizing all irreducible representations of the symmetric groups. This theory is then used to answer questions concerning to central projections in the …