2023/07/13 by Dimitry Gurevich, Pavel Saponov, Gurevich, Dimitry +1 · 1 citation
Chemistry · Mathematics · #05E05 (Primary) #20C08 (Secondary) #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Molecular spectroscopy and chirality #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2307.06677
openalex publication_date 2023/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a q-version of the Schur-Weyl duality, in which the role of the symmetric group is played by the Hecke algebra and the role of the enveloping algebra U(gl(N)) is played by the Reflection Equation algebra, associated with any skew-invertible Hecke symmetry. Also, in each Reflection Equation algebra we define analogues of the Schur polynomials and power sums in two forms: as polynomials in generators of a given Reflection Equation algebra and in terms of the so-called eigenvalues of the generating matrix L, defined by means of the Cayley-Hamilton identity. It is shown that on any Reflection Equation algebra there exists a formula, which brings into correlation the Schur polynomials and power sums by means of the characters of the Hecke algebras in the spirit of the classical Frobenius formula.