Equivariant prime ideals for infinite dimensional supergroups

Autor: Laudone, Robert P., Snowden, Andrew

Let $A$ be a commutative algebra equipped with an action of a group $G$. The so-called $G$-primes of $A$ are the equivariant analogs of prime ideals, and of central importance in equivariant commutative algebra. When $G$ is an infinite dimensional gr

Externí odkaz: http://arxiv.org/abs/2103.03152

Sp-equivariant modules over polynomial rings in infinitely many variables

Autor: Sam, Steven V, Snowden, Andrew

Publikováno v: Trans. Amer. Math. Soc. 375 (2022), 1671-1701

We study the category of Sp-equivariant modules over the infinite variable polynomial ring, where Sp denotes the infinite symplectic group. We establish a number of results about this category: for instance, we show that every finitely generated modu

Externí odkaz: http://arxiv.org/abs/2002.03243

Noetherianity of some degree two twisted commutative algebras

Autor: Nagpal, Rohit, Sam, Steven V, Snowden, Andrew

Publikováno v: Selecta Math. (N.S.) 22 (2016), no. 2, 913-937

In recent years, researchers have discovered various large algebraic structures that have surprising finiteness properties, such as FI-modules and Delta-modules. In this paper, we add another example to the growing list: we show that certain degree t

Externí odkaz: http://arxiv.org/abs/1501.06925

On the geometry and representation theory of isomeric matrices

Autor: Nagpal, Rohit, Sam, Steven V, Snowden, Andrew

Publikováno v: Algebra & Number Theory. 16:1501-1529

The space of $n \times m$ complex matrices can be regarded as an algebraic variety on which the group ${\bf GL}_n \times {\bf GL}_m$ acts. There is a rich interaction between geometry and representation theory in this example. In an important paper,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ad55b65c7e15327326d5fad9f929182a
https://doi.org/10.2140/ant.2022.16.1501

Noetherianity of some degree two twisted skew-commutative algebras

Autor: Rohit Nagpal, Steven V Sam, Andrew Snowden

Publikováno v: Selecta Mathematica, vol 25, iss 1
Nagpal, Rohit; Sam, Steven V; & Snowden, Andrew. (2019). Noetherianity of some degree two twisted skew-commutative algebras. SELECTA MATHEMATICA-NEW SERIES, 25(1). doi: 10.1007/s00029-019-0461-3. UC San Diego: Retrieved from: http://www.escholarship.org/uc/item/5kf8c71t
Selecta Mathematica, New Series, vol 25, iss 1

A major open problem in the theory of twisted commutative algebras (tca's) is proving noetherianity of finitely generated tca's. For bounded tca's this is easy, in the unbounded case, noetherianity is only known for Sym(Sym^2(C^\infty)) and Sym(\wedg

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c2199bfec685ff76232be870fa2f3d82