Degenerate principal series of quantum Harish-Chandra modules

In this paper we study a quantum analogue of a degenerate principal series of $U_q \mathfrak{su}_{n,n}$-modules ($0<q<1$) related to the Shilov boundary of the quantum $n \times n$-matrix unit ball. We give necessary and sufficient conditions for the modules to be simple and unitarizable and investigate their equivalence. These results are q-analogues of known classical results on reducibility and unitarizability of SU(n,n)-modules obtained by Johnson, Sahi, Zhang, Howe and Tan.Comment: 33 pages, 4 figure

Stein--Sahi complementary series and their degenerations

The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n,n).Comment: 40pp, 7fig, revised versio

Impact Assessment of Mercury Accumulation and Biochemical and Molecular Response of Mentha arvensis

The present study was focused on examining the effect of Hg oxidative stress induced physiochemical and genetic changes in M. arvensis seedlings. The growth rate of Hg treated seedlings was decreased to 56.1% and 41.5% in roots and shoots, respectively, compared to the control. Accumulation of Hg level in both roots and shoots was increased with increasing the concentration of Hg. Superoxide dismutase (SOD), catalase (CAT), and ascorbate peroxidase (APX) activities were found to be increased with increasing the Hg concentration up to 20 mg/L; however, it was decreased at 25 mg/L Hg concentration. The POX enzyme activity was positively correlated with Hg dose. The changes occurring in the random amplification of ploymorphic DNA (RAPD) profiles generated from Hg treated seedlings included variations in band intensity, disappearance of bands, and appearance of new bands compared with the control seedlings. It was concluded that DNA polymorphisms observed with RAPD profile could be used as molecular marker for the evaluation of heavy metal induced genotoxic effects in plant species. The present results strongly suggested that Mentha arvensis could be used as a potential phytoremediator plant in mercury polluted environment

Derivatives for smooth representations of GL(n,R) and GL(n,C)

The notion of derivatives for smooth representations of GL(n) in the p-adic case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations by S. Sahi and called the "adduced" representation. In this paper we define derivatives of all order for smooth admissible Frechet representations (of moderate growth). The archimedean case is more problematic than the p-adic case; for example arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation. In [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS12].Comment: First version of this preprint was split into 2. The proofs of two theorems which are technically involved in analytic difficulties were separated into "Twisted homology for the mirabolic nilradical" preprint. All the rest stayed in v2 of this preprint. v3: version to appear in the Israel Journal of Mathematic

The effects of advanced maternal age on T- cell subsets at the maternal- fetal interface prior to term labor and in the offspring: a mouse study

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/155904/1/cei13437.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155904/2/cei13437_am.pd

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Generalized Second Law of Thermodynamics on the Event Horizon for Interacting Dark Energy

Here we are trying to find the conditions for the validity of the generalized second law of thermodynamics (GSLT) assuming the first law of thermodynamics on the event horizon in both cases when the FRW universe is filled with interacting two fluid system- one in the form of cold dark matter and the other is either holographic dark energy or new age graphic dark energy. Using the recent observational data we have found that GSLT holds both in quintessence era as well as in phantom era for new age graphic model while for holographic dark energy GSLT is valid only in phantom era.Comment: 8 pages, 2 figure

The Fourth BATSE Gamma-Ray Burst Catalog (Revised)

The Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory (CGRO) has triggered on 1637 cosmic gamma-ray bursts between 1991 April 19 and 1996 August 29. These events constitute the Fourth BATSE burst catalog. The current version (4Br) has been revised from the version first circulated on CD-ROM in September 1997 (4B) to include improved locations for a subset of bursts that have been reprocssed using additional data. A significant difference from previous BATSE catalogs is the inclusion of bursts from periods when the trigger energy range differed from the nominal 50-300 keV. We present tables of the burst occurrence times, locations, peak fluxes, fluences, and durations. In general, results from previous BATSE catalogs are confirmed here with greater statistical significance.Comment: 45 pages, 12 Postscript figures, accepted for publication in Ap. J. Supp

Quantum symmetric pairs and representations of double affine Hecke algebras of type C∨CnC^\vee C_n

We build representations of the affine and double affine braid groups and Hecke algebras of type $C^\vee C_n$, based upon the theory of quantum symmetric pairs $(U,B)$. In the case $U=U_q(gl_N)$, our constructions provide a quantization of the representations constructed by Etingof, Freund and Ma in arXiv:0801.1530, and also a type $BC$ generalization of the results in arXiv:0805.2766.Comment: Final version, to appear in Selecta Mathematic