2,970 research outputs found
A plethysm formula for p\sb µ(\underline x)\circ h\sb \lambda(\underline x)
A previous paper by the author \ref["A new plethysm formula for symmetric functions", J. Algebraic Combin., submitted] expresses the plethysm of the power sum symmetric function and the complete symmetric function, , as a sum of Schur functions with coefficients that are roots of unity. The paper under review extends this result to , where the complete symmetric function is indexed by a partition rather than an integer. Specifically, the author proves that for a partition of and a partition of with length , , where the sum is over semistandard tableaux of weight and is a root of unity. The proof is inductive and employs an intermediate result proved using the jeu de taquin
Modular Invariants for Lattice Polarized K3 Surfaces
We study the class of complex algebraic K3 surfaces admitting an embedding of
H+E8+E8 inside the Neron-Severi lattice. These special K3 surfaces are
classified by a pair of modular invariants, in the same manner that elliptic
curves over the field of complex numbers are classified by the J-invariant. Via
the canonical Shioda-Inose structure we construct a geometric correspondence
relating K3 surfaces of the above type with abelian surfaces realized as
cartesian products of two elliptic curves. We then use this correspondence to
determine explicit formulas for the modular invariants.Comment: 29 pages, LaTe
Lattice Polarized K3 Surfaces and Siegel Modular Forms
The goal of the present paper is two-fold. First, we present a classification
of algebraic K3 surfaces polarized by the lattice H+E_8+E_7. Key ingredients
for this classification are: a normal form for these lattice polarized K3
surfaces, a coarse moduli space and an explicit description of the inverse
period map in terms of Siegel modular forms. Second, we give explicit formulas
for a Hodge correspondence that relates these K3 surfaces to principally
polarized abelian surfaces. The Hodge correspondence in question underlies a
geometric two-isogeny of K3 surfaces
A Superfield for Every Dash-Chromotopology
The recent classification scheme of so-called adinkraic off-shell
supermultiplets of N-extended worldline supersymmetry without central charges
finds a combinatorial explosion. Completing our earlier efforts, we now
complete the constructive proof that all of these trillions or more of
supermultiplets have a superfield representation. While different as
superfields and supermultiplets, these are still super-differentially related
to a much more modest number of minimal supermultiplets, which we construct
herein.Comment: 13 pages, integrated illustration
- …