Quantum determinants and categorification of quantum groups

• Grant number: 15/05927-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2016
• End date: February 28, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Vyacheslav Futorny
• Grantee: Jian Zhang
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 14/09310-5 - Algebraic structures and their representations, AP.TEM

Abstract

The main goal of this project is to study quantumdeterminants and quantum Pfaffians in the type B_n, C_n, D_n and relate it to the categorification of quantum groups. (AU)

Scientific publications

(9)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FUTORNY, VYACHESLAV; RAMIREZ, LUIS ENRIQUE; ZHANG, JIAN. Gelfand-Tsetlin representations of finite W-algebras. Journal of Pure and Applied Algebra, v. 224, n. 5, MAY 2020. (15/05927-0, 14/09310-5, 18/17955-7)

FUTORNY, VYACHESLAV; SERGANOVA, VERA; ZHANG, JIAN. Gelfand-Tsetlin modules for gl(m|n). MATHEMATICAL RESEARCH LETTERS, v. 28, n. 5, p. 40-pg., 2021-01-01. (15/05927-0, 18/23690-6)

JING, NAIHUAN; ZHANG, JIAN. Capelli identity on multiparameter quantum linear groups. SCIENCE CHINA-MATHEMATICS, v. 61, n. 2, p. 16-pg., 2018-02-01. (15/05927-0)

JING, NAIHUAN; ZHANG, JIAN. Capelli identity on multiparameter quantum linear groups. SCIENCE CHINA-MATHEMATICS, v. 61, n. 2, SI, p. 253-268, FEB 2018. (15/05927-0)

FUTORNY, VYACHESLAV; RAMIREZ, LUIS ENRIQUE; ZHANG, JIAN. Gelfand-Tsetlin modules of quantum gl(n) defined by admissible sets of relations. Journal of Algebra, v. 499, p. 375-396, APR 1 2018. (14/09310-5, 15/05927-0)

FUTORNY, VYACHESLAV; RAMIREZ, LUIS ENRIQUE; ZHANG, JIAN. Irreducible subquotients of generic Gelfand-Tsetlin modules over U-q(gl(n)). Journal of Pure and Applied Algebra, v. 222, n. 10, p. 3182-3194, OCT 2018. (15/05927-0, 14/09310-5)

FUTORNY, VYACHESLAV; RAMIREZ, LUIS ENRIQUE; ZHANG, JIAN. Explicit construction of irreducible modules for U-q(gl(n)). SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 13, n. 1, p. 83-95, JUN 2019. (15/05927-0, 14/09310-5, 18/17955-7)

FUTORNY, VYACHESLAV; KRIZKA, LIBOR; ZHANG, JIAN. Quantum Howe duality and invariant polynomials. Journal of Algebra, v. 530, p. 326-367, JUL 15 2019. (15/05927-0, 14/09310-5)

FUTORNY, VYACHESLAV; KRIZKA, LIBOR; ZHANG, JIAN. Generalized Verma Modules over U-q(sl(n)(C)). ALGEBRAS AND REPRESENTATION THEORY, v. 23, n. 3, p. 811-832, JUN 2020. (15/05927-0, 14/09310-5)