4,480 research outputs found
Modular transformations of admissible N = 2 and Affine sl(2|1;C) characters
Get PDFThis thesis is a study of the affine super-algebra sl(2|l; C) and N = 2 superconformal algebra at fractional levels. In the first chapter we review background material on Conformal Field Theory, and how it appears in the context of string theory and the Wess - Zumino – Novikov - Witten model. We also discuss integrable and admissible representations of infinite dimensional algebras and their modular transformations. In Chapter 2 we elaborate some more on modular transformations and we derive them in the case of non - unitary minimal N = 2 characters. Some very explicit formulas are presented. In Chapter 3 we discuss character formulas for the affine sl(2|l;C) algebra and some of their general properties are given, in particular their behaviour under spectral flow. In Chapter 4 we turn to the study of sumrules for sl(2|l;C) at level k. These involve the product of sl(2) characters at level k, k', and 1 with {k + l){k' + !) = 1. We consider k + 1 = for = 1, p e Z*, u eN and show that the sumruleswe have obtained agree with the literature when the parameter p is restricted to p = 1. We use the integral form of the sumrules to study the modular properties of sl(2|l) characters at fractional level in the last section of Chapter 4.The advisor for this work has been Dr. Anne Taormina
CR1 Knops blood group alleles are not associated with severe malaria in the Gambia
No full textThe Knops blood group antigen erythrocyte polymorphisms have been associated with reduced falciparum malaria-based in vitro rosette formation (putative malaria virulence factor). Having previously identified single-nucleotide polymorphisms (SNPs) in the human complement receptor 1 (CR1/CD35) gene underlying the Knops antithetical antigens Sl1/Sl2 and McC(a)/McC(b), we have now performed genotype comparisons to test associations between these two molecular variants and severe malaria in West African children living in the Gambia. While SNPs associated with Sl:2 and McC(b+) were equally distributed among malaria-infected children with severe malaria and control children not infected with malaria parasites, high allele frequencies for Sl 2 (0.800, 1,365/1,706) and McC(b) (0.385, 658/1706) were observed. Further, when compared to the Sl 1/McC(a) allele observed in all populations, the African Sl 2/McC(b) allele appears to have evolved as a result of positive selection (modified Nei-Gojobori test Ka-Ks/s.e.=1.77, P-valu
Aspects of the affine superalgebra sl(2|1) at fractional level
Get PDFAspects of the Affine Superalgebra sl(2|l) at Fractional Level Ph.D. Thesis by Gavin Balfour Johnstone, April 2001 In this thesis we study the affine superalgebra sl(2|l; C) at fractional levels of the form k = l/u-l,uєN\{l}. It is for these levels that admissible representations exist, which transform into each other under modular transformations. In the second chapter we review background material on conformal field theory, particularly the Wess-Zumino-Witten model and the connection with modular transformations. The superalgebra sl(2|l;C) is introduced, as is its affine version. The next chapter studies the modular transformation properties of sl(2|l;C) characters. We derive formulae for these transformations for all levels of the form K = 1/u-1,uєN\{1}. We also investigate some modular invariant combinations of characters and find two series of modular invariants, analogous to the A- and D-series of the classification of sl{2) modular invariants. In chapter 4 we turn to the study of fusion rules. We concentrate on the case k = -1/2. By considering the decoupling of singular vectors, we are able to find consistent fusion rules for this particular level. These fusion rules correspond to a modular invariant found in chapter 3. This study suggests that one may consistently define a conformal field theory based on sl(2|l;C) at fractional level
Quantum and its irreducible representations
Get PDFWe define for real a unital -algebra
quantizing the universal enveloping
-algebra of . The -algebra
is realized as a -subalgebra of the
Drinfeld double of and its dual Hopf -algebra
, generated by the equatorial Podle\'s sphere coideal
-subalgebra of and
its associated orthogonal coideal -subalgebra . We then classify all the irreducible
-representations of .Comment: 22 pages; author accepted manuscrip
On the sheaf-theoretic SL(2, C) Casson–Lin invariant
No full textWe prove that the (τ-weighted, sheaf-theoretic) SL(2, C) Casson–Lin invariant introduced by Manolescu and the first author is generically independent of the parameter τ and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions asked by Manolescu and the first author. Our arguments involve a mix of topology and algebraic geometry, and rely crucially on the fact that the SL(2, C) Casson–Lin invariant admits an alternative interpretation via the theory of Behrend functions.</p
Candidatus Rhetoricae (or Novus Candidatus).
No full textThis little book is a find whatever it finally turns out to be! For now it seems to be a Jesuit collegium text in rhetoric following the Progymnasmata of Aphthonius. If one works from the back of the book, there is an apparently independent 48-page work, Angelus Pacis by Nicolas Caussini (Latinized name), S.J. The rest of the book seems to be a commentary on or presentation of Aphthonius' Progymnasmata in 3 parts covering 435 pages, followed by a T of C and an AI, which is often one page off. Pars II is titled Rhetoricae Praecepta, Pars III De Panegyrico seu Laudatione. Pars I seems to be Apparatus ad Fabulam et Narrationem. Fable is handled on 15-31. After the famous Greek definition of Theion done into Latin ( sermo falsus veritatem effingens ), the author distinguishes rational (human) and moral (animal) fables, with mixed fables including both. He holds (19) that the sense of the fable generally needs to be expressed; otherwise people often miss the point of a fable. His Latin for promythium is praefabulatio, for epimythium affabulatio. Apologus and parabola are identical for him with fabula. After describing the qualities and uses of fables, the author presents some nine fables that exemplify various levels of style, twice telling the same stories on two levels (WL and FC). The last example is of the florid style: The Silkworm and the Spider takes four pages to tell! I found this book sitting in a box of disparate, unmarked, old books. It pays to look!This is a hardbound book (hard cover)Language note: Bilingual: Greek/LatinElzevers
Searches for New Physics effects in b →sl-sl+ transitions
No full textThe dissertation aims at presenting the current situation in the measurements of electroweak
penguin diagrams dominated decays: b → sl−l+1 . These decays have been a smoking gun
for hunting for New Physics effects over many years, but in the last three years the research
on these phenomena has intensified due to new measurements. Enormous progress has
been made both on the theoretical and the experimental sides to understand the measured
deviations from the current Standard Model predictions, referred to in what follows as
“anomalies”. The author of this dissertation has been one of the main authors of the angular analysis
of B0→ K∗ 0µ+µ− decay in the LHCb experiment, which has been widely regarded as one
of the most important results of the flavour physics sector in recent years. He has proposed
a method called “the method of moments” to measure the angular terms of this decay,
which he has later successfully applied in the measurement itself. Moreover, he has been
the driving force behind the two other important analyses in LHCb: the measurement of
the angular distribution and branching ratio of the B0→ K∗ 0 (1430)µ+µ− decay, where again the method of moments has been used to obtain the angular coefficients, and the search for the light scalar particle that can be produced in the b → s transitions and that decays to a dimuon pair. In this case no signal has been observed and the upper limits on the branching fraction have been set, later to be used for constraining the inflaton model.
The dissertation is organized as follows: the brief introduction is followed by, the second
chapter devoted to a theoretical description of rare B decays, where the effective field
theory formalism is introduced. Furthermore, the author discusses the current theoretical
problems in calculating the Standard Model predictions for the b → sl−l+ processes. Last but not least, the optimised angular observables that are less dependent on the form
factors uncertainness are derived. The third chapter describes the experimental apparatus
used in the b → sl−l+ measurements. Special focus is put on the sub-detectors that play
an important role in the studies of b → sl−l+ transitions. Chapters 4, 5, 6 are devoted to
describing the data analyses performed by the author in the LHCb experiment. In Chapter 7
the global analysis of electroweak penguin decays is presented. This kind of global analysis
has become extremely popular in the past few years as it helps to constrain and pin down those New Physics models that are likely to be responsible for the observed anomalies. The
author of this monograph is involved in one of the biggest collaborations performing New
Physics fits, where he is the convenor of the Flavour Working group. Furthermore, the
author presents his own study on separating the long distance effects in the B0→ K∗ 0µ+µ−decay. This is the state of the art way of determining those contributions. The chapter ends with a description of possible New Physics models that can explain the observed discrepancies
contravariant function-valued valuations on polytopes
Get PDFWe present a complete classification of contravariant,
-valued valuations on polytopes, without any
additional assumptions.It extends the previous results of the second author
[Int. Math. Res. Not. 2020] which have a good connection with the and
Orlicz Brunn-Minkowski theory. Additionally, our results deduce a complete
classification of contravariant symmetric-tensor-valued
valuations on polytopes
The Laurent Extension of Quantum Plane: a Complete List of Uq(sl₂)-Symmetries
No full textThis work finishes a classification of Uq(sl₂)-symmetries on the Laurent extension Cq[x±¹,y±¹] of the quantum plane. After reproducing the partial results of a previous paper of the author related to symmetries with non-trivial action of the Cartan generator(s) of Uq(sl₂) and the generic symmetries, a complete collection of non-generic symmetries is presented. Together, these collections constitute a complete list of Uq(sl₂)-symmetries on Cq[x±¹,y±¹].The author would like to thank the anonymous referees for a large number of comments and suggestions that substantially improved the initial version of this paper
Constructing Thin Subgroups in SL(4, R)
Get PDFWe give a construction for new families of thin subgroups inside SL(4,R). In particular, we show that the fundamental group of a closed hyperbolic 3-manifold can be isomorphic to a thin subgroup of a lattice. © The Author(s) 2013
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