26,139 research outputs found
Modular transformations of admissible N = 2 and Affine sl(2|1;C) characters
No full textThis 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
Adjoint representations for SU(2), su(2) and sl(2)
No full textThis work, presents four kinds of adjoint representations for the special unitary matrix Lie group SU(2) and the special unitary, special linear matrix Lie algebras su(2) and sl(2). In the first two we assume the vector spaces as the matrix Lie algebras su(2) and sl(2), later cases obtained by exploiting the action of su(2) and sl(2) on themselves. Also, we compute their direct sums. The results have been displayed as Tables in a nice form
Adjoint representations for SU(2), su(2) and sl(2)
No full textThis work, presents four kinds of adjoint representations for the special unitary matrix Lie group SU(2) and the special unitary, special linear matrix Lie algebras su(2) and sl(2). In the first two we assume the vector spaces as the matrix Lie algebras su(2) and sl(2), later cases obtained by exploiting the action of su(2) and sl(2) on themselves. Also, we compute their direct sums. The results have been displayed as Tables in a nice form.</jats:p
SU (2) and SL(2, C) Representations of a Class of Torus Knots
No full textAbstract: Let Km,2 be the torus knot of type (m, 2). With the help of the explicit description of the SL(2, C) character variety of this class of torus knots given by the author in a previous work, we study the relationship between the representations over SU (2) and over SL(2, C) of the fundamental group of S 3 \ Km,2. In particular it is shown that the map from the moduli space of irreducible SU (2)-representations to the moduli space of SL(2, C)-representations is injective
SU(2) and SL(2, ℂ) representations of a class of torus Knots
No full textLet Km;2 be the torus knot of type (m, 2). With the help of the explicit description of the SL(2, ℂ) character variety of this class of torus knots given by the author in a previous work, we study the relationship between the representations over SU(2) and over
SL(2, ℂ) of the fundamental group of S³ \ K ₘ,₂. In particular it is shown that the map from the moduli space of irreducible SU(2)-representations to the moduli space of
SL(2, ℂ)-representations is injective.peerReviewe
REPRESENTASI su(2) DAN KOMPLEKSIFIKASI su(2)_C=sl(2,C) PADA RUANG VEKTOR POLINOM HOMOGEN
No full textAljabar Lie su(N) mempunyai kompleksifikasi sl(N,C). Dengan kata lain, suNC≅sl(N,C). Dalam artikel ini, dipelajari representasi aljabar Lie su(N) dan sl(N,C) khususnya untuk N=2 yang direalisasikan pada ruang vektor polinom homogen kompleks dua variabel berderajat dua. Tujuannya adalah untuk mengkonstruksi representasi sl(2,C) dari representasi su(2) dan membuktikan bahwa representasi yang diperoleh bersifat unitar dan tak tereduksi. Selanjutnya, karena grup Lie dari su(2) bersifat simply connected maka representasi su(2) dapat dikonstruksi dari grup Lie-nya. Di sisi lain, karena su2C≅sl(2,C) maka representasi dari sl(2,C) dapat dikonstruksi melalui perluasan linear-kompleks dari representasi su(2) dan hasilnya dapat dinyatakan dalam bentuk operator linear
Quantum and its irreducible representations
No full textWe 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
Couplings of Brownian motions on and
No full textThe Lie groups and can be viewed as model spaces
in subRiemannian geometry. Coupling two subelliptic Brownian motions on
(resp. ) consists in coupling two Brownian motions on the
sphere (resp. the hyperbolic plane) and simultaneously their swept areas. Using
this approach we propose an explicit construction of a co-adapted successful
coupling on . The strategy is to alternate between reflection and
synchronous (with noise) coupling on the sphere. We also describe some more
general constructions of co-adapted couplings on and also on
Couplings of Brownian motions on and
No full textThe Lie groups and can be viewed as model spaces in subRiemannian geometry. Coupling two subelliptic Brownian motions on (resp. ) consists in coupling two Brownian motions on the sphere (resp. the hyperbolic plane) and simultaneously their swept areas. Using this approach we propose an explicit construction of a co-adapted successful coupling on . The strategy is to alternate between reflection and synchronous (with noise) coupling on the sphere. We also describe some more general constructions of co-adapted couplings on and also on
Factors associated with the diagnosis of neurodevelopmental disorders: a population-based longitudinal study
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