Composition Factors of Polynomial Representation of DAHA and Crystallized Decomposition Numbers

2006/04/17 by Naoya Enomoto, Enomoto, Naoya
Mathematics · #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.math/0604368

openalex publication_date 2006/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the composition factors of the polynomial representation of DAHA, conjectured by M. Kasatani. We reduce the determination of composition factors of polynomial representations of DAHA to the determination of the composition factors of the Weyl module W⁽¹ⁿ⁾ for the v-Schur algebra. By using the LLT-Ariki type theorem of v-Schur algebra proved by Varagnolo-Vasserot, we determine the composition factors of W⁽¹ⁿ⁾ by calculating the upper global basis and crystal basis of Fock space of U_q(\mfsl_ℓ).

Citations

• From double affine Hecke algebras to quantized affine Schur algebras
• Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras
• Decomposition numbers and canonical bases

Related

• Decomposition numbers and canonical bases
• Multiplicity matrices for the affine graded Hecke algebra
• An efficient algorithm computing composition factors of T(V)^{⊗ n}
• Decomposition numbers of quantized walled Brauer algebras
• Product formulas for the cyclotomic v-Schur algebra and for the canonical bases of the Fock space