Constructing invariants for finite groups.
Decomposition of the diagonal action of on the coinvariant space of .
Der Endlichkeitssatz der Invarianten endlicher Gruppen.
Die Isomorphie der Invariantenkörper der endlichen Abelschen Gruppen lineaerer Transformatioen
Dunkl operators and canonical invariants of reflection groups.
Etale covers, bimodules and differential operators.
Étude des jets de Demailly-Semple en dimension 3
Dans cet article nous faisons l’étude algébrique des jets de Demailly-Semple en dimension 3 en utilisant la théorie des invariants des groupes non réductifs. Cette étude fournit la caractérisation géométrique du fibré des jets d’ordre 3 sur une variété de dimension 3 et permet d’effectuer, par Riemann-Roch, un calcul de caractéristique d’Euler.
Factorial extensions of regular local rings and invariants of finite groups.
Finite generating system of matrix invariants.
-Invariant tensors and graphs
We describe a correspondence between -invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.
Global structure of the mod two symmetric algebra, over the Steenrod Algebra.
Groups with large Noether bound
The finite groups having an indecomposable polynomial invariant of degree at least half the order of the group are classified. It turns out that –apart from four sporadic exceptions– these are exactly the groups with a cyclic subgroup of index at most two.
Ideal class (semi)groups and atomicity in Prüfer domains
We explore the connection between atomicity in Prüfer domains and their corresponding class groups. We observe that a class group of infinite order is necessary for non-Noetherian almost Dedekind and Prüfer domains of finite character to be atomic. We construct a non-Noetherian almost Dedekind domain and exhibit a generating set for the ideal class semigroup.
Invariant theory and the algebra with negative integral central charge
The vertex algebra with central charge may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer , it was conjectured in the physics literature that should have a minimal strong generating set consisting of elements. Using a free field realization of due to Kac–Radul, together with a deformed version of Weyl’s first and second fundamental theorems of invariant theory for the standard representation of ,...
Invariant theory of a class of infinite-dimensional groups.
Invariants for the modular cyclic group of prime order via classical invariant theory
Let be any field of characteristic . It is well-known that there are exactly inequivalent indecomposable representations of defined over . Thus if is any finite dimensional -representation there are non-negative integers such that . It is also well-known there is a unique (up to equivalence) dimensional irreducible complex representation of given by its action on the space of forms. Here we prove a conjecture, made by R. J. Shank, which reduces the computation of the ring...
Invariants of finite groups generated by generalized transvections in the modular case
We investigate the invariant rings of two classes of finite groups which are generated by a number of generalized transvections with an invariant subspace over a finite field in the modular case. We name these groups generalized transvection groups. One class is concerned with a given invariant subspace which involves roots of unity. Constructing quotient groups and tensors, we deduce the invariant rings and study their Cohen-Macaulay and Gorenstein properties. The other is concerned with...
Irreducible linear group-subgroup pairs with the same invariants.
Locally finite iterative higher derivations on k[x,y]
We give a new proof of Miyanishi's theorem on the classification of the additive group scheme actions on the affine plane.
Noether's problem for some groups of order 16n