Linear representations, symmetric products and the commuting scheme
نویسندگان
چکیده
منابع مشابه
Linear representations, symmetric products and the commuting scheme
We show that the ring of multisymmetric functions over a commutative ring is isomorphic to the ring generated by the coefficients of the characteristic polynomial of polynomials in commuting generic matrices. As a consequence we give a surjection from the ring of invariants of several matrices to the ring of multisymmetric functions generalizing a classical result of H.Weyl and F.Junker. We als...
متن کاملSymmetric products, linear representations and the commuting scheme I: isomorphisms and embeddings
We show that the symmetric product of a flat affine scheme over a commutative ring can be embedded into the quotient by the general linear group of the scheme of commuting matrices. We also prove that the symmetric product of the affine space is isomorphic to the above quotient when the base ring is a characteristic zero field. Over an infinite field of arbitrary characteristic the quotient of ...
متن کاملModuli of linear representations, symmetric products and the non commutative Hilbert scheme
Let k be a commutative ring and let R be a commutative k−algebra. Given a positive integer n and a R−algebra A one can consider three functors of points from the category CR of commutative R−algebras to the small category of sets. All these functors are representable, namely • RepA represents the functor induced by B → homR(A,Mn(B)), where Mn(B) are the n× n matrices over B, for all B ∈ CR. • t...
متن کاملThe Sums and Products of Commuting AC-Operators
Abstract: In this paper, we exhibit new conditions for the sum of two commuting AC-operators to be again an AC-operator. In particular, this is satisfied on Hilbert space when one of them is a scalar-type spectral operator.
متن کاملDiscrete torsion, symmetric products and the Hilbert scheme
Recently the understanding of the cohomology of the Hilbert scheme of points on K3 surfaces has been greatly improved by Lehn and Sorger [18]. Their approach uses the connection of the Hilbert scheme to the orbifolds given by the symmetric products of these surfaces. We introduced a general theory replacing cohomology algebras or more generally Frobenius algebras in a setting of global quotient...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.06.033