Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Khoroshkin, Anton"'
The celebrated Cauchy identity expresses the product of terms $(1 - x_i y_j)^{-1}$ for $(i,j)$ indexing entries of a rectangular $m\times n$-matrix as a sum over partitions $\lambda$ of products of Schur polynomials: $s_{\lambda}(x)s_{\lambda}(y)$. A
Externí odkaz:
http://arxiv.org/abs/2411.03117
Autor:
Khoroshkin, Anton, Lyskov, Denis
Contractads are operadic-type algebraic structures well-suited for describing configuration spaces indexed by a simple connected graph $\Gamma$. Specifically, these configuration spaces are defined as $\mathrm{Conf}_{\Gamma}(X):=X^{|V(\Gamma)|}\setmi
Externí odkaz:
http://arxiv.org/abs/2406.05909
The main goal of this paper is to categorify the specialized parasymmetric (intermediate) Macdonald polynomials. These polynomials depend on a parabolic subalgebra of a simple Lie algebra and generalize the symmetric and nonsymmetric Macdonald polyno
Externí odkaz:
http://arxiv.org/abs/2311.12673
We study the algebra of functions on the Iwahori group via the category of graded bounded representations of its Lie algebra. In particular, we identify the standard and costandard objects in this category with certain generalized Weyl modules. Using
Externí odkaz:
http://arxiv.org/abs/2307.02124
We show that the tensor product of modules of tensor fields is a noetherian module as a module over any graded Lie subalgebra of finite codimension in the Lie algebra of polynomial vector fields on $\mathbb{R}^n$. As a corollary, we prove the conject
Externí odkaz:
http://arxiv.org/abs/2211.08510
Autor:
Khoroshkin, Anton, Merkulov, Sergei
We study the deformation complex of the dg wheeled properad of $\mathbb{Z}$-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the Grothendieck-Teichm
Externí odkaz:
http://arxiv.org/abs/2109.07793
We describe a categorification of the Double Affine Hecke Algebra (${\mathcal{H}\kern -.4em\mathcal{H}}$) associated with an affine Lie algebra $\widehat{\mathfrak{g}}$, including a categorification of the polynomial representation and Macdonald poly
Externí odkaz:
http://arxiv.org/abs/2103.10009
In this work we provide a definition of a coloured operad as a monoid in some monoidal category, and develop the machinery of Gr\"obner bases for coloured operads. Among the examples for which we show the existance of a quadratic Gr\"obner basis we c
Externí odkaz:
http://arxiv.org/abs/2008.05295
Autor:
Khoroshkin, Anton, Tamaroff, Pedro
We define derived Poincar\'e--Birkhoff--Witt maps of dg operads or derived PBW maps, for short, which extend the definition of PBW maps between operads of V.~Dotsenko and the second author in 1804.06485, with the purpose of studying the universal env
Externí odkaz:
http://arxiv.org/abs/2003.06055
Autor:
Dotsenko, Vladimir, Khoroshkin, Anton
We show that the celebrated operad of pre-Lie algebras is very rigid: it has no "non-obvious" degrees of freedom from either of the three points of view: deformations of maps to and from the "three graces of operad theory", homotopy automorphisms, an
Externí odkaz:
http://arxiv.org/abs/2002.12918