相关论文: Explicit construction of companion bases
This paper computes the obstruction to the existence of equivariant extensions of basic gerbes over non-simply connected compact simple Lie groups. By modifying a (finite dimensional) construction of Gaw\c{e}dzki-Reis [J. Geom. Phys.…
The twistor construction is applied for obtaining examples of generalized complex structures (in the sense of N. Hitchin) that are not induced by a complex or a symplectic structure.
We develop a mutation theory for quivers with oriented 2-cycles using a structure called a homotopy, defined as a normal subgroupoid of the quiver's fundamental groupoid. This framework extends Fomin-Zelevinsky mutations of 2-acyclic…
We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. As an…
We use the Kempf-Lascoux-Weyman geometric technique in order to determine the minimal free resolutions of some orbit closures of quivers. As a consequence, we obtain that for Dynkin quivers orbit closures of 1-step representations are…
Motivated to simplify the structure of tensor representations we give a new set of generators for the Yangian $Y(sl(n))$ using the principal realization in simple Lie algebras. The isomorphism between our new basis and the standard…
We provide an elementary consistency proof of Quine's New Foundations, by a construction using interated nominal powersets.
The Dowker complex is an abstract simplicial complex that is constructed from a binary relation in a straightforward way. Although there are two ways to perform this construction -- vertices for the complex are either the rows or the…
The aim of this paper is to present a very simple original, purely formal, proof of Quillen's adjunction theorem for derived functors, and of some more recent variations and generalizations of this theorem. This is obtained by proving an…
Coherent strings of composable morphisms play an important role in various important constructions in abstract stable homotopy theory (for example algebraic K-theory or higher Toda brackets) and in the representation theory of finite…
Degeneracy loci polynomials for quiver representations generalize several important polynomials in algebraic combinatorics. In this paper we give a nonconventional generating sequence description of these polynomials, when the quiver is of…
This paper E3 shows how to construct the simplest Exotic Invariant in the simplest way.
With the aid of the creation operators introduced in our previous works, we show how to construct a basis of the space of quasi-local operators for the homogeneous XXZ chain.
We present a simple bijection between permutation matrices and descending plane partitions without special parts. This bijection is already mentioned in work of P. Lalonde (without giving the details); it involves the inversion words of…
The dynamics of large complex systems are predominately modeled through pairwise interactions, the principle underlying structure being a network of the form of a digraph or quiver. Significant success has been obtained in applying the…
For a Dynkin quiver $Q$ of type ADE and a sum $\beta$ of simple roots, we construct a bimodule over the quantum loop algebra and the quiver Hecke algebra of the corresponding type via equivariant K-theory, imitating…
We construct three compatible quadratic Poisson structures such that generic linear combination of them is associated with Elliptic Sklyanin algebra in n generators. Symplectic leaves of this elliptic Poisson structure is studied. Explicit…
In 1990 Beilinson, Lusztig and MacPherson provided a geometric realization of modified quantum $\mathfrak{gl}_n$ and its canonical basis. A key step of their work is a construction of a monomial basis. Recently, Du and Fu provided an…
This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals…
We show how affine PBW bases can be used to construct affine MV polytopes, and that the resulting objects agree with the affine MV polytopes recently constructed using either preprojective algebras or KLR algebras. To do this we first…