2016/02/29 by Shiyuan Liu, Liu, Shiyuan
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.1602.08792
arxiv created 2016/02/29 · openalex publication_date 2016/02/29 · arxiv updated 2016/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The X=M conjecture asserts that the 1D sum and the fermionic formula coincide up to some constant power. In the case of type A, both the 1D sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials K\Bla,\Bmu(t), indexed by two double partitions \Bla,\Bmu, are polynomials in t introduced as a generalization of Kostka polynomials. In the present paper, we consider K\Bla,\Bmu(t) in the special case where \Bmu=(-,μ''). We formulate a 1D sum and a fermionic formula for K\Bla,\Bmu(t), as a generalization of the case of ordinary Kostka polynomials. Then we prove an analogue of the X=M conjecture.