• 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 17 REFERENCES
Syzygies of Determinantal Thickenings and Representations of the General Linear Lie Superalgebra
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
The syzygies of some thickenings of determinantal varieties
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}
Dualities and Representations of Lie Superalgebras
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
Generalised Jantzen filtration of Lie superalgebras I
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
Cohomology of Vector Bundles and Syzygies
1. Introduction 2. Schur functions and Schur complexes 3. Grassmannians and flag varieties 4. Bott's theorem 5. The geometric technique 6. The determinantal varieties 7. Higher rank varieties 8. The
Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup
We prove that blocks of the general linear supergroup are Morita equivalent to a limiting version of Khovanov's diagram algebra. We deduce that blocks of the general linear supergroup are Koszul.
...
...