Young Walls of Type D^(2)_n+1 and Strict Partitions

2011/05/12 by Se‐jin Oh, Oh, Se-jin · 1 citation
Mathematics · #05A17 #17B37 #17B65 #81R50 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1105.2380

openalex publication_date 2011/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the number of reduced Young walls of type D_n+1⁽²⁾ with m blocks is independent of n and the same as the number of strict partitions of m. Thus the principally specialized character χ_n^Λ₀(t) of V(Λ₀) over U_q(D_n+1⁽²⁾) can be interpreted as a generating function for strict partitions. Hence we obtain an infinite family of generalizations of Euler's partition identity.

Cited by

• Schur partition theorems via perfect crystal

Related

• Sequences of odd length in strict partitions II: the 2-measure and refinements of Euler's theorem
• Fixed perimeter analogues of some partition results
• On Glaisher's Partition Theorem
• Enumeration of Even Dimensional Partitions modulo 4
• Generalizations of Euler's Theorem to k-regular partitions