We give a generating function for the number of pairs n×n matrices (A,B) over finite field that are mutually annihilating, namely, AB=BA=0. This can be viewed as singular analogue series considered by Cohen and Lenstra. show this has factorization allows it to meromorphically extended entire complex plane. also use count annihilating nilpotent matrices. work is essentially study motivic aspects...

Book Reviews classical medical training. Following a six year apprenticeship in an English country surgery and a brief period in London, he returned to Berkeley in 1792 to practice variolation, a method that had been popularized to com-The Eradication of Small Pox: Edward bat the smallpox. As the author points out, variolation Jenner and the First and Only Eradication was a highly dangerous pra...

Let V be a vector space over some field k, and let α : V V be a linear map (an ‘endomorphism of V ’). Given any polynomial p with coefficients in k, there is an endomorphism p(α) of V , and we say that p is an annihilating polynomial for α if p(α) = 0. Our first major goal is to see that for any α, the annihilating polynomials can easily be classified: they’re precisely the multiples of a certa...

We use Kazhdan-Lusztig tensoring to, first, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA and, second, to classify tilting functors, an affine analogue of projective functors known in the case of a simple Lie algebra.

For an untwisted affine Kac-Moody Lie algebra g̃, and a given positive integer level k, vertex operators x(z) = ∑ x(n)z−n−1, x ∈ g, generate a vertex operator algebra V . For the maximal root θ and a root vector xθ of the corresponding finite-dimensional g, the field xθ(z) k+1 generates all annihilating fields of level k standard g̃-modules. In this paper we study the kernel of the normal order p...