Flag manifolds and the Landweber-Novikov algebra

We investigate geometrical interpretations of various structure maps associated with the Landweber-Novikov algebra S^* and its integral dual S_*. In particular, we study the coproduct and antipode in S_*, together with the left and right actions of S^* on S_* which underly the construction of the quantum (or Drinfeld) double D(S^*). We set our realizations in the context of double complex cobordism, utilizing certain manifolds of bounded flags which generalize complex projective space and may be canonically expressed as toric varieties. We discuss their cell structure by analogy with the classical Schubert decomposition, and detail the implications for Poincare duality with respect to double cobordism theory; these lead directly to our main results for the Landweber-Novikov algebra.Comment: 23 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper5.abs.htm

Introduction: Special issue on genetic research of alcohol use disorder in diverse racial/ethnic populations

This special issue of The American Journal on Addictions is an extension of a workshop held at the Research Society on Alcoholism (2015) highlighting several important issues related to studies of the genetic bases of alcohol use disorder among racially/ethnically diverse populations. While not exhaustive in their coverage, the papers in this special issue focus on three important topics: (1) the importance of considering the social and environmental context in genetic analyses; (2) social and cultural considerations for engaging diverse communities in genetic research; and (3) methodologies related to phenotype development for use with racially/ethnically diverse populations. A brief overview of each paper included in these three sections is presented. The issue concludes with additional considerations for genetic research with racially/ethnically diverse population groups along with a commentary. (Am J Addict 2017;26:422–423

Theory of the high-frequency chiral optical response in a p_x+ip_y superconductor

The optical Hall conductivity and the polar Kerr angle are calculated as functions of temperature for a two-dimensional chiral p_x+ip_y superconductor, where the time-reversal symmetry is spontaneously broken. The theoretical estimate for the polar Kerr angle agrees by the order of magnitude with the recent experimental measurement in Sr2RuO4 by Xia et al. cond-mat/0607539. The theory predicts that the Kerr angle is proportional to the square of the superconducting energy gap and is inversely proportional to the cube of frequency, which can be verified experimentally.Comment: 4 pages, no figures, RevTeX. V.2: one reference and discussion of horizontal lines of nodes added. V.3: a typo corrected, and one reference added. V.4: two references added and minor stylistic changes made, as in the published versio

Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid

Recent experiments on the organic compound \kappa-(ET)_2Cu_2(CN)_3 have provided a promising example of a two dimensional spin liquid state. This phase is described by a two-dimensional spinon Fermi sea coupled to a U(1) gauge field. We study Kohn-Luttinger-like pairing instabilities of the spinon Fermi surface due to singular interaction processes with twice-the-Fermi-momentum transfer. We find that under certain circumstances the pairing instability occurs in odd-orbital-angular-momentum/spin-triplet channels. Implications to experiments are discussed.Comment: 4 pages, 1 figur

Irreducible modules over finite simple Lie conformal superalgebras of type K

We construct all finite irreducible modules over Lie conformal superalgebras of type KComment: Accepted for publication in J. Math. Phys