We study the notion of weak one-basedness introduced in recent work of Berenstein and Vassiliev. Our main results are that this notion characterises linearity in the setting of geometric þ-rank 1 structures and that lovely pairs of weakly one-based geometric þ-rank 1 structures are weakly one-based with respect to þ-independence. We also study geometries arising from infinite dimensional vector...

In this paper, we obtain infinitely many non-trivial identities and inequalities between full rank differences for 2-marked Durfee symbols, a generalization of partitions introduced by Andrews. A certain strict inequality, which almost always holds, shows that identities for Dyson’s rank, similar to those proven by Atkin and Swinnerton-Dyer, are quite rare. By showing an analogous strict inequa...

We construct and study in detail various dual pairs acting on some Fock spaces between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite affine Cartan matrix. We give explicit decompositions of a Fock representation into a direct sum of irreducible isotypic subspaces with respect to the action of a dual pair, present explicit formulas for the ...

Let E/Q be an elliptic curve defined over Q of conductor N and let Gal(Q/Q) be the absolute Galois group of an algebraic closure Q of Q. For an automorphism σ ∈ Gal(Q/Q), we let Q be the fixed subfield of Q under σ. We prove that for every σ ∈ Gal(Q/Q), the Mordell-Weil group of E over the maximal Galois extension of Q contained in Q σ has infinite rank, so the rank of E(Q σ ) is infinite. Our ...

We investigate the connection between the abelian rank of a countable amenable group and the existence of good averaging sequences (eg for the ergodic theorem). We show that if G is a group with finite abelian rank r(G), then 2 is a lower bound on the constant associated to a Tempel’man sequence, and if G is abelain there is a Tempel’man sequence in G with this constant. On the other hand, infi...

Moufang sets are split doubly transitive permutation groups, or equivalently, groups with a split BN-pair of rank one. In this paper, we study so-called special Moufang sets with abelian root groups, under the model-theoretic restriction that the groups have finite Morley rank. These groups have a natural base field, and we classify them under the additional assumption that the base field is in...

Mappings between certain infinite series of N = 2 superconformal coset models are constructed. They make use of level-rank dualities for B, C and D type WZW theories, which are described in some detail. The WZW level-rank dualities do not constitute isomorphisms of the theories; for example, for B and D type WZW theories, only simple current orbits rather than individual primary fields are mapp...

We consider the prediction of weak effects in a multiple-output regression setup, when covariates are expected to explain a small amount, less than ≈ 1%, of the variance of the target variables. To facilitate the prediction of the weak effects, we constrain our model structure by introducing a novel Bayesian approach of sharing information between the regression model and the noise model. Furth...

We investigate the average sizes of the n largest fragments in nuclear multifragmentation events near the critical point of the nuclear matter phase diagram. We perform analytic calculations employing Poisson statistics as well as Monte Carlo simulations of the percolation type. We find that previous claims of manifestations of Zipf’s Law in the rank-ordered fragment size distributions are not ...