2025/10/08 by Pallav Goyal, Goyal, Pallav, Daniele Rosso +1
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2510.07469
openalex publication_date 2025/10/08 · openalex created_date 2025/10/11 · openalex updated_date 2026/08/01
We show that the mirabolic quantum group MU(n) is a comodule algebra over the quantized enveloping algebra Uv(\mathfraksln), and use this structure to give a complete classification of its finite dimensional representations. In particular, we explicitly describe the construction of all irreducible finite dimensional representations of MU(n) and show that the category of finite dimensional representations is semisimple. A crucial step involves constructing and analyzing Verma-type universal representations of MU(n).