Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of Minkowski space-time. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations for n=6, including the necessary data for all relevant invariant differential operators. In fact, this gives by reduction also the cases for n<6, since the main multiplet for fixed n coincides with one reduced case for n+1.Comment: Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:0812.2690, arXiv:0812.265

The evolution of organizational niches : U.S. automobile manufacturers, 1885-1981.

Although the niche figures prominently in contemporary theories of organization, analysts often fail to tie micro processes within the niche to long-term changes in the broader environment. In this paper, we advance arguments about the relationship between an organization's niche and evolution in the structure of its organizational population over time. We focus on the technological niche and processes of positioning and crowding among firms in the niche space, relating them to the level of concentration among all firms in the market. Building on previous empirical studies in organizational ecology, we study the evolution of concentration in the American automobile industry from 1885 to 1981 and estimate models of the hazard of exit of individual producers from the market. The findings show that niche and concentration interact in complex ways, yielding a more unified depiction of organizational evolution than typically described or reported

Representation Theory Approach to the Polynomial Solutions of q - Difference Equations : U_q(sl(3)) and Beyond,

A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a q - difference realization of U_q(sl(n)) in terms of n(n-1)/2 commuting variables and depending on n-1 complex representation parameters r_i, is constructed. From this realization lowest weight modules (LWM) are obtained which are studied in detail for the case n=3 (the well known n=2 case is also recovered). All reducible LWM are found and the polynomial bases of their invariant irreducible subrepresentations are explicitly given. This also gives a classification of the quasi-exactly solvable operators in the present setting. The invariant subspaces are obtained as solutions of certain invariant q - difference equations, i.e., these are kernels of invariant q - difference operators, which are also explicitly given. Such operators were not used until now in the theory of polynomial solutions. Finally the states in all subrepresentations are depicted graphically via the so called Newton diagrams.Comment: uuencoded Z-compressed .tar file containing two ps files

Anomalies, Unparticles, and Seiberg Duality

We calculate triangle anomalies for fermions with non-canonical scaling dimensions. The most well known example of such fermions (aka unfermions) occurs in Seiberg duality where the matching of anomalies (including mesinos with scaling dimensions between 3/2 and 5/2) is a crucial test of duality. By weakly gauging the non-local action for an unfermion, we calculate the one-loop three-current amplitude. Despite the fact that there are more graphs with more complicated propagators and vertices, we find that the calculation can be completed in a way that nearly parallels the usual case. We show that the anomaly factor for fermionic unparticles is independent of the scaling dimension and identical to that for ordinary fermions. This can be viewed as a confirmation that unparticle actions correctly capture the physics of conformal fixed point theories like Banks-Zaks or SUSY QCD.Comment: 13 pages, 1 figur

The G protein-gated potassium current I(K,ACh) is constitutively active in patients with chronic atrial fibrillation

Background— The molecular mechanism of increased background inward rectifier current (IK1) in atrial fibrillation (AF) is not fully understood. We tested whether constitutively active acetylcholine (ACh)-activated IK,ACh contributes to enhanced basal conductance in chronic AF (cAF). Methods and Results— Whole-cell and single-channel currents were measured with standard voltage-clamp techniques in atrial myocytes from patients with sinus rhythm (SR) and cAF. The selective IK,ACh blocker tertiapin was used for inhibition of IK,ACh. Whole-cell basal current was larger in cAF than in SR, whereas carbachol (CCh)-activated IK,ACh was lower in cAF than in SR. Tertiapin (0.1 to 100 nmol/L) reduced IK,ACh in a concentration-dependent manner with greater potency in cAF than in SR (−logIC50: 9.1 versus 8.2; P<0.05). Basal current contained a tertiapin-sensitive component that was larger in cAF than in SR (tertiapin [10 nmol/L]-sensitive current at −100 mV: cAF, −6.7±1.2 pA/pF, n=16/5 [myocytes/patients] versus SR, −1.7±0.5 pA/pF, n=24/8), suggesting contribution of constitutively active IK,ACh to basal current. In single-channel recordings, constitutively active IK,ACh was prominent in cAF but not in SR (channel open probability: cAF, 5.4±0.7%, n=19/9 versus SR, 0.1±0.05%, n=16/9; P<0.05). Moreover, IK1 channel open probability was higher in cAF than in SR (13.4±0.4%, n=19/9 versus 11.4±0.7%, n=16/9; P<0.05) without changes in other channel characteristics. Conclusions— Our results demonstrate that larger basal inward rectifier K+ current in cAF consists of increased IK1 activity and constitutively active IK,ACh. Blockade of IK,ACh may represent a new therapeutic target in AF

Positive Energy Representations, Holomorphic Discrete Series and Finite-Dimensional Irreps

Let G be a semi-simple non-compact Lie group with unitary lowest/highest weight representations. We consider explicitly the relation between three types of representations of G: positive energy (unitary lowest weight)representations, (holomorphic) discrete series representations and non-unitary finite-dimensional irreps. We consider mainly the conformal groups SO(n,2) treating in full detail the cases n=1,3,4.Comment: 28 pages, TEX with Harvmac using amssym.def, amssym.tex, epsf.tex; v2: new texts in Sections 1 & 3, new refs; v3: added 5 figures; v4: small correction

ON SOME ASPECTS IN ULTRASONOGRAPHY OF THE UPPER ABDOMEN

No abstrac

Positive Energy Unitary Irreducible Representations of the Superalgebras osp(1|2n,R)

We give the classification of the positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R).Comment: 20 pages, LATEX2e (revtex4,amsmath,amssymb), Plenary talk by VKD at X International Conference on Symmetry Methods in Physics, Yerevan, 13-21.8.2003; added acknowledgements; corrected misprint