Related papers: A generalization of the Capelli identity
In this note we give a generalization of the well-known Menon's identity. This is based on applying the Burnside's lemma to a certain group action.
Inspired by the Capelli identities for group determinants obtained by T\^oru Umeda, we give a basis of the center of the group algebra of any finite group by using Capelli identities for irreducible representations. The Capelli identities…
We classify up to isomorphism the quantum generalized Weyl algebras and determine their automorphism groups in all cases in a uniform way, including those where the parameter q is a root of unity, thereby completing the results obtained by…
We prove a duality theorem for quantum groupoid (weak Hopf algebra) actions that extends the well-known result for usual Hopf algebras.
Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related…
We show how the use of superalgebraic methods sheds new light on some classical themes of representation theory and it leads to significant simplifications of traditional proofs.
The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of the GL(m|n) type.
A generalization $\mathfrak{Gal}_{\ell}(p,q)$ of the conformal Galilei algebra $\mathfrak{g}_{\ell}(d)$ with Levi subalgebra isomorphic to $\mathfrak{sl}(2,\mathbb{R})\oplus\mathfrak{so}(p,q)$ is introduced and a virtual copy of the latter…
We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states that the lattice of all boolean algebras of regular languages…
We extend the concept of a partial group action to non-associative algebras in a variety \(\mathcal{V}(I)\), solve the globalization problem within \(\mathcal{V}(I)\) and examine its universal property. It is achieved using what we call the…
One discovers why the solution of generalized umbral calculus difference nonhomogeneous equation in the form recently proposed by the author extends here now to generalized appellian delta operator and corresponding polynomials case almost…
Using jagged overpartitions, we give three generalizations of a weighted word version of Capparelli's identity due to Andrews, Alladi, and Gordon and present several corollaries.
We give an accessible and modern description of the automorphisms of a finite abelian group $G$. Included is an explicit formula for the cardinality of $Aut(G)$.
We construct a canonical isomorphism between the Bethe algebra acting on a multiplicity space of a tensor product of evaluation gl_N[t]-modules and the scheme-theoretic intersection of suitable Schubert varieties. Moreover, we prove that…
We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties
A family of general integral identities is derived and several applications of physical interest are presented
We consider the concept of a generalised manifold in the O(d,d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are…
Generalizing the known results on graded rings and modules, we formulate and prove the equivariant version of the local duality on schemes with a group action. We also prove an equivariant analogue of Matlis duality.
We propose a generalization of Bailey's lemma, useful for proving $q$-series identities. As an application, generalizations of Euler's identity, the Rogers-Ramanujan identities, and the Andrews-Gordon identities are derived. This…
In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.