Minor Identities for Quasideterminants and Quantum Determinants

Abstract

We present several identities involving quasi-minors of noncommutative generic matrices. These identities are specialized to quantum matrices, yielding q-analogues of various classical determinantal formulas.

24 pages tex dialect: LaTex

References in corpus (2)

• Noncommutative symmetric functions
• Yangians and Classical Lie Algebras

Cited by in corpus (41)

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• R-Matrix presentation of quantum affine algebra in type $A_{2n-1}^{(2)}$
• Spin characters of hyperoctahedral wreath products
• Quantum Hyperdeterminants and Hyper-Pfaffians
• Twisted q-Yangians and Sklyanin determinants
• Flag varieties for the Yangian Y(gl_n)
• Matrix Orthogonal Polynomials, non-abelian Toda lattice and Bäcklund transformation
• Skew representations of twisted Yangians
• Localizations for construction of quantum coset spaces
• Quantum determinants and quasideterminants
• Twisting the quantum grassmannian
• Quantum algebra of multiparameter Manin matrices
• Noncommutative Shifted Symmetric Functions
• Yangians and transvector algebras
• Quantum Berezinian for quantum affine superalgebra $U_q({\widehat{gl}}_{M|N})$
• Application of quasideterminants to the inverse of block triangular matrices over noncommutative rings
• A simple algorithm for extending the identities for quantum minors to the multiparametric case
• Quantum- and Quasi-Plucker Coordinates
• Quasi-Commuting Families of Quantum Minors
• Commutation relations for arbitrary quantum minors