About Gelfand-Tsetlin Patterns

A Gelfand-Tsetlin pattern (GT-pattern) is a triangular array of integers satisfying the interlacing condition:

Each entry must lie between the two entries directly above it. The top row λ defines a partition, and GT-patterns parameterize the irreducible representations of GL_n(ℂ).

The number of valid patterns with a fixed top row λ equals the dimension of the corresponding representation.