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of 103
pro vyhledávání: '"Zadunaisky, P."'
We provide an explicit combinatorial realization of all simple and injective (hence, and projective) modules in the category of bounded $\mathfrak{sp}(2n)$-modules. This realization is defined via a natural tableaux correspondence between spinor-type
Externí odkaz:
http://arxiv.org/abs/2406.15929
Autor:
Zadunaisky, Pablo
We study a category of modules over $\mathfrak{gl}(\infty)$ analogous to category $\mathcal O$. We fix adequate Cartan, Borel and Levi-type subalgebras $\mathfrak h, \mathfrak b$ and $\mathfrak l$ with $\mathfrak l \cong \mathfrak{gl}(\infty)^n$, and
Externí odkaz:
http://arxiv.org/abs/2205.04874
Autor:
Zadunaisky, Pablo
We show that every finite non-degenerate set theoretical solution to the YBE whose retraction is a flip linearizes to a twist of the flip solution by roots of unity. This generalizes a result of Gateva-Ivanova and Majid. To prove the result we use a
Externí odkaz:
http://arxiv.org/abs/2110.03988
Autor:
Rigal, Laurent, Zadunaisky, Pablo
We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen-Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry, this can b
Externí odkaz:
http://arxiv.org/abs/1902.07675
We introduce the notion of essential support of a simple Gelfand-Tsetlin $\mathfrak{gl}_n$-module as an important tool towards understanding the character formula of such module. This support detects the weights in the module having maximal possible
Externí odkaz:
http://arxiv.org/abs/1811.07992
In the present paper we study Gelfand-Tsetlin modules defined in terms of BGG differential operators. The structure of these modules is described with the aid of the Postnikov-Stanley polynomials introduced in [PS09]. These polynomials are used to id
Externí odkaz:
http://arxiv.org/abs/1801.09316
A Gelfand-Tsetlin tableau $T(v)$ induces a character $\chi_v$ of the Gelfand-Tsetlin subalgebra $\Gamma$ of $U = U(\mathfrak{gl}(n,\mathbb C))$. By a theorem due to Ovsienko, for each tableau $T(v)$ there exists a finite number of nonisomorphic irred
Externí odkaz:
http://arxiv.org/abs/1705.10731
Autor:
Solotar, Andrea, Zadunaisky, Pablo
Let $G,H$ be groups, $\phi: G \rightarrow H$ a group morphism, and $A$ a $G$-graded algebra. The morphism $\phi$ induces an $H$-grading on $A$, and on any $G$-graded $A$-module, which thus becomes an $H$-graded $A$-module. Given an injective $G$-grad
Externí odkaz:
http://arxiv.org/abs/1703.08721
Autor:
Zadunaisky, Pablo
We present a simplified way to construct the Gelfand-Tsetlin modules over $\mathfrak{gl}(n,\mathbb C)$ related to a $1$-singular GT-tableau defined by Futorny, Grantcharov and Ramirez. We begin by reframing the classical construction of generic Gelfa
Externí odkaz:
http://arxiv.org/abs/1703.07264
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