• Corpus ID: 221006117

# Syzygies of Determinantal Thickenings

@article{Huang2020SyzygiesOD,
title={Syzygies of Determinantal Thickenings},
author={Hang Huang},
journal={arXiv: Commutative Algebra},
year={2020}
}
• Hang Huang
• Published 6 August 2020
• Mathematics
• arXiv: Commutative Algebra
Let $S = \mathbb{C}[x_{i,j}]$ be the ring of polynomial functions on the space of $m \times n$ matrices, and consider the action of the group $\mathbf{GL} = \mathbf{GL}_m \times \mathbf{GL}_n$ via row and column operations on the matrix entries. It is proven by Raicu and Weyman that for a $\mathbf{GL}$-invariant ideal $I \subseteq S$, the linear strands of its minimal free resolution translates via the BGG correspondence to modules over the general linear Lie superalgebra $\mathfrak{gl}(m|n… ## References SHOWING 1-10 OF 18 REFERENCES Syzygies of Determinantal Thickenings and Representations of the General Linear Lie Superalgebra • Mathematics Acta Mathematica Vietnamica • 2018 We let S=ℂ[xi,j]$S=\mathbb C[x_{i,j}]$denote the ring of polynomial functions on the space of m×n$m\times n$matrices and consider the action of the group GL=GLm×GLn$\text {GL}=\text {GL}_{m}\times
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The syzygies of some thickenings of determinantal varieties
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• 2014
The vector space of m x n complex matrices (m >= n) admits a natural action of the group GL = GL_m x GL_n via row and column operations. For positive integers a,b, we consider the ideal I_{a x b}
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We prove that integral blocks of parabolic category O associated to the subalgebra gl(m) x gl(n) of gl(m+n) are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras. Although
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• Mathematics
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This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation
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• 2010
A Jantzen type filtration for generalised Varma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac