For a finite subgroup $\Gamma\subset {\mathrm{SL}}(2,\mathbb{C})$, we identify fine moduli spaces of certain cornered quiver algebras, defined in earlier work, with orbifold Quot schemes for the Kleinian $[\mathbb{C}^2/\Gamma]$. We also describe reduced underlying these as Nakajima varieties framed McKay $\Gamma$, taken at specific non-generic stability parameters. These are therefore irreducib...

For a finite subgroup $\Gamma\subset \mathrm{SL}(2,\mathbb{C})$ and $n\geq 1$, we construct the (reduced scheme underlying the) Hilbert of $n$ points on Kleinian singularity $\mathbb{C}^2/\Gamma$ as Nakajima quiver variety for framed McKay $\Gamma$, taken at specific non-generic stability parameter. We deduce that this is irreducible (a result previously due to Zheng), normal, admits unique sym...

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

First, recall how Bezout’s Theorem can be made more precise by specifying the meaning of the word “generically” used above, using elementary scheme-theoretic language ([H, II]). Fix an algebraically closed field k. There is little loss in assuming k = C (until Section 3). Since we work over an algebraically closed field, we often identify reduced algebraic sets with their k-valued points. In th...

We review and motivate recently-observed relationships between exactly solvable lattice models and modular representations of Hecke algebras. Firstly, we describe how the set of n-regular partitions label both of the following classes of objects: 1. The spectrum of unrestricted solid-on-solid lattice models based on level-1 representations of the affine algebras ŝln, 2. The irreducible represen...

The factorial-additive optimality of primes, i.e., that the sum prime factors is always minimum, implies numbers are a solution to an integer linear programming (ILP) encoding optimization problem. summative primes follows from Goldbach’s conjecture, and viewed as upper efficiency limit for any with fewest possible additions. A consequence above optimally encode—multiplicatively additively—all ...

Let $M$ be a complex manifold. We prove that compact submanifold $S\subset M$ with splitting tangent sequence (called submanifold) is rational homogeneous when in large class of spaces Picard number one. Moreover, irreducible Hermitian symmetric, we $S$ must also symmetric. The basic tool use the restriction and projection map $\pi$ global holomorphic vector fields on ambient space which induce...

In 1936 G. T. Whyburn [8] defined an irreducible mapping to be a mapping/, of a compact metric continuum A onto B, such that no proper sub-continuum of A maps onto B under/. Similarly, assuming A to be only compact and metric, he defined / to be strongly irreducible provided that no closed proper subset of A maps onto B. J. Rozanska [7] independently defined this second type of mapping in 1937....