2026 Fall / 2026.09.22.
Thrall's problem for two rows
초록
Thrall’s problem (1942) asks for a combinatorial Schur expansion of the character of the higher Lie module Lλ. Prior to this work it was known only for one row, one column, and two columns. We solve the two-row case λ = (n, n): the coefficient of sμ in ch(Lλ) counts standard Young tableaux of shape μ satisfying a block-major-index condition, refined by a spin parity inherited from Yamanouchi domino tableaux via Carré–Leclerc and van Leeuwen. The same framework yields formulas for hooks, distinct-parts shapes, and all partitions in which each part greater than 2 appears at most twice. This is joint work with JiSun Huh, Woo-Seok Jung, and Meesue Yoo.
Abstract
Thrall’s problem (1942) asks for a combinatorial Schur expansion of the character of the higher Lie module Lλ. Prior to this work it was known only for one row, one column, and two columns. We solve the two-row case λ = (n, n): the coefficient of sμ in ch(Lλ) counts standard Young tableaux of shape μ satisfying a block-major-index condition, refined by a spin parity inherited from Yamanouchi domino tableaux via Carré–Leclerc and van Leeuwen. The same framework yields formulas for hooks, distinct-parts shapes, and all partitions in which each part greater than 2 appears at most twice. This is joint work with JiSun Huh, Woo-Seok Jung, and Meesue Yoo.
Video Link
