We present a group theoretic construction of the Virasoro algebra in the framework of wreath products. This can be regarded as a counterpart of a geometric construction of Lehn in the theory of Hilbert schemes of points on a surface. Introduction It is by now well known that a direct sum ⊕ n≥0R(Sn) of the Grothendieck rings of symmetric groups Sn can be identified with the Fock space of the Hei...

Note that the map π is equivariant under the Gm-action, where the Gm-action on A2 is by dilation. When k is a field of positive characteristic, for simplicity, we denote A2n(1) simply by V and denote Hilb(A2)(1) by X. As has been explained in [Vain14], for any integral weight λ of G, on X there is a quantization OX , coming from quantum Hamiltonian reduction of D(g⊕ An), the sheaf of differenti...

If R is a ring of coefficients and G a finite group, then a flat RG-module which is projective as an R-module is necessarily projective as an RG-module. More generally, if H is a subgroup of finite index in an arbitrary group Γ, then a flat RΓmodule which is projective as an RH-module is necessarily projective as an RΓ-module. This follows from a generalization of the first theorem to modules o...

A systematical study on the early X-ray afterglows of both optically bright and dark gamma-ray bursts (B-GRBs and D-GRBs) observed by Swift has been presented. Our sample includes 25 GRBs. Among them 13 are B-GRBs and 12 are D-GRBs. Our results show that the distributions of the X-ray afterglow fluxes (FX), the gamma-ray fluxes (Sγ), and the ratio (Rγ,X) for both the D-GRBs and B-GRBs are simil...

We develop dimension theory for a large class of structures of the form (L,≤,⊥,∼), where (L ≤) is a partially ordered set, ⊥ is a binary relation on L, and ∼ is an equivalence relation on L, subject to certain axioms. We call these structures espaliers. For x, y, z ∈ L, we say that z = x ⊕ y holds, if x ⊥ y and z is the supremum of {x, y}. The dimension theory of L is the universal ∼-invariant ...

We present a group theoretic construction of the Virasoro algebra in the framework of wreath products. This can be regarded as a counterpart of a geometric construction of Lehn in the theory of Hilbert schemes of points on a surface. Introduction It is by now well known that a direct sum ⊕ n≥0R(Sn) of the Grothendieck rings of symmetric groups Sn can be identified with the Fock space of the Hei...