Abstract
A formula for the number of Gelfand-Zetlin patterns
Highlights
Suppose Λ = (a1, a2, . . . , an−1) is a sequence of decreasing non-negative integers
A GelfandZetlin pattern based on Λ is an array of integers: a1
The set ΓΛ has an important role in the representation theory of general and orthogonal linear Lie algebras
Summary
We denote the set of all Gelfand-Zetlin patterns based on Λ by ΓΛ. Let Λ be a dominant weight for the Lie algebra sln(C) and suppose L(Λ) is the corresponding irreducible representation with the highest weight Λ. The set ΓΛ is important from the point of view of branching rules. Branching rules are descriptions of the reduction of irreducible representations upon restriction to a subalgebra (subgroup). We can employ the set ΓΛ to describe the branching rule for type sln(C) → slr(C). Suppose we like to restrict the representation L(Λ) to slr(C). Let χπ be the irreducible character of the symmetric group Sm corresponding to π, (for standard terms about partitions and characters of Sm, see [11]).
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