Related papers: On Noether's and Weyl's bound in positive characte…

Max Noether's Theorem asserts that if $\ww$ is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve then the natural morphisms $\text{Sym}^nH^0(\omega)\to H^0(\omega^n)$ are surjective for all $n\geq 1$. This is true for…

We provide a geometric extension of the generalized Noether theorem for scaling symmetries recently presented in \cite{zhang2020generalized}. Our version of the generalized Noether theorem has several positive features: it is constructed in…

An important problem from invariant theory is to describe the subspace of a tensor power of a representation invariant under the action of the group. According to Weyl's classic, the first main (later: 'fundamental') theorem of invariant…

We prove a reduced version of the Chevalley restriction conjecture on the commuting scheme posed by T.H. Chen and B.C. Ng\^o, extending the results of Hunziker for classical groups. In particular, we prove that for any connected reductive…

Noether's problem is classical and very important problem in algebra. It is an intrinsically interesting problem in invariant theory, but with far reaching applications in the sutdy of moduli spaces, PI-algebras, and the Inverse problem of…

We consider a finite permutation group acting naturally on a vector space $V$ over a field $\Bbbk$. A well known theorem of G\"obel asserts that the corresponding ring of invariants $\Bbbk[V]^G$ is generated by invariants of degree at most…

We define the graph minor category and prove that the category of contravariant representations of the graph minor category over a Noetherian ring is locally Noetherian. This can be regarded as a categorification of the Robertson--Seymour…

Using the weak factorization theorem we give a simple presentation for the value group of the universal Euler characteristic with compact support for varieties of characteristic zero and describe the value group of the universal Euler…

The best known method to give a lower bound for the Noether number of a given finite group is to use the fact that it is greater than or equal to the Noether number of any of the subgroups or factor groups. The results of the present paper…

We develop a representation theoretic technique for detecting closed orbits that is applicable in all characteristics. Our technique is based on Kempf's theory of optimal subgroups and we make some improvements and simplify the theory from…

We study systems of parameters over finite fields from a probabilistic perspective, and use this to give the first effective Noether normalization result over a finite field. Our central technique is an adaptation of Poonen's closed point…

We prove a non-generosity theorem for proper cosets in groups of finite Morley rank and elaborate on the theory of Weyl groups in this context.

We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally compact groups possessing large…

We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic approach. In both classical and quantum mechanics, observables…

This is the first of a series of papers where we develop a theory of total positivity for loop groups. In this paper, we completely describe the totally nonnegative part of the polynomial loop group GL_n(\R[t,t^{-1}]), and for the formal…

Noether's theorem and the invariances of the Willmore functional are used to derive conservation laws that are satisfied by the critical points of the Willmore energy subject to generic constraints. We recover in particular previous results…

Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and…

We give a geometric proof of a theorem of Weyl on the continuous part of the spectrum of Sturm-Liouville operators on the half-line with asymptotically constant coefficients. Earlier proofs due to Weyl and Kodaira depend on special features…

It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In…

Bochner's theorem characterizes positive definite functions on groups through the positivity of their Fourier transforms and plays a fundamental role in Harmonic analysis. While Bochner-type results are known for certain classes of…