140,064 research outputs found
A remark on rational Cherednik algebras and differential operators on the cyclic quiver
Get PDFWe show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn 2 Cl, the wreath product of the symmetric group and the cyclic group of order l, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size l. This confirms a version of [5, Conjecture 11.22] in the case of cyclic groups. The proof is a straightforward application of work of Oblomkov [12] on the deformed Harish–Chandra homomorphism, and of Crawley–Boevey, [3] and [4], and Gan and Ginzburg [7] on preprojective algebras
On the categories of Harish-Chandra modules
Get PDFGiven an algebra A, the study of the category of A-modules is often restricted to the study of
a more tractable subcategory of A-modules which are well-behaved with respect to a subalgebra Γ
of A. In 1973, Lepowsky and McCollum studied the category of A-modules which are weight
modules with respect to Γ. Later, in 1994, Drozd, Futorny, and Ovsienko studied the category of
A-modules which are generalized weight modules with respect to Γ, called Harish-Chandra
modules. They showed that the structure of Harish-Chandra modules can be described using
information about the relationship between A and the cofinite maximal ideals of Γ.
In Chapter 2 of this thesis, we generalize the framework of Drozd, Futorny, and Ovsienko by
introducing an equivalence relation ∼ on the set cfs(Γ) of cofinite maximal ideals of Γ. We define
Harish-Chandra block modules with respect to ∼ to be A-modules that are the direct sum of block
spaces corresponding to the equivalence classes cfs(Γ)/∼. We describe the structure of
Harish-Chandra block modules based on the relationship between A and cfs(Γ)/∼. In particular,
we give decompositions of the category of Harish-Chandra block modules and the collection of
isomorphism classes of simple Harish-Chandra block modules. We also define a topologically
enriched category A with objects cfs(Γ)/∼, and show the category of Harish-Chandra block
modules is equivalent to a category of continuous A-modules. Furthermore, we provide a
sufficient condition for when there are a finite number of isomorphism classes of simple
Harish-Chandra block modules with a given support.
In Chapter 3, we continue the study of (generalized) Harish-Chandra modules. We observe
that the equivalence of categories obtained in Chapter 2 is closely related to a Yoneda embedding.
We begin to define a Harish-Chandra pair as a pair (A, B) where A is an algebra, and B is a full
subcategory of AMod. We review some potential examples, and identify the presence of a left adjoint to the Yoneda embedding Y : AMod → [Bop, Vectk] as a key property. In many cases, we
can describe the subcategories on which this adjunction is an equivalence
Classification of simple Harish-Chandra modules over Q-Virasoro algebra
No full textWe give a complete classification of simple Harish-Chandra modules over Q - Virasoro algebra. 1 Introduction A classification of the simple Harish-Chandra modules over complex Virasoro algebra V was given by O.Mathieu in remarkable paper [7]. According to this classification each simple Harish-Chandra V-module is either highest (lowest) weight module or module from the so-called intermediate series. There exist a lot of different generalizations of the classical Virasoro algebra and centerless Virasoro algebra (Witt algebra) studied by several authors (see for example [4, 5, 9, 10, 11]). Naturally there appears a question to give a classification of HarishChandra modules over all those algebras. In the subsequent paper we consider the following generalization of the Virasoro algebra which is called Q - Virasoro algebra. We define G to be a Lie algebra with the base fe(x) j x 2 Qg [ fcg and the Lie brackets given by [e(x); e(y)] = (y \Gamma x)e(x + y) + ffi x;\Gammay x 3 \Gamma x ..
Harish Chandra modules of rank one lie groups with admissible restriction to some reductuve subgroup
Get PDFThis note determine the irreducible Harish Chandra modules of a rank one semisimple Lie group with admissible restriction to some proper reductive subgroup.Fil: Vargas, Jorge Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin
Pareto-optimized modulation formats for suppression of stimulated Brillouin scattering in optical fiber amplifiers
No full textWith the help of a robust model for stimulated Brillouin scattering (SBS) in Yb-doped fiber amplifiers, we Pareto-optimize phase modulation formats for suppressing SBS. We achieved 1.6 times enhancement in SBS threshold for 100MHz linewidth.<br/
Harish Chandra modules of rank one lie groups with admissible restriction to some reductuve subgroup
Get PDFThis note determine the irreducible Harish Chandra modules of a rank one semisimple Lie group with admissible restriction to some proper reductive subgroup.Fil: Vargas, Jorge Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin
34 Lalita Harish Nikam Indian
No full textAbstract To study Salt Taste Threshold (STT) and its relation to Blood pressure (BP) in normotensive adolescents, age and BMI matched 60 subjects of 18-20 years were segregated on basis of family history of hypertension, documented risk factor for development of hypertension. Student's unpaired t-test showed that STT and BP values were significantly higher in Hypertensive offspring group than Control. Pearson Chi Square test with 60 mM Nacl as cut-off point showed highly significant association of STT in hypertensive offspring group. A significant positive correlation was found between STT and BP by Pearson correlation analysis. Family history of hypertension is strongly linked to reduced salt taste sensitivity. This reinforces rationale that both conditions may be genetically linked though causal relation cannot be established. STT can be used as significant marker to screen 'salt sensible' subjects that eventually will develop hypertension and can be advised healthy habits early or prophylactically treated. Indian J Physiol Pharmacol 2015; 59(1) : 34-40 T h e r e i s s t i l l m u c h u n c e r t a i n t y a b o u t t h e pathophysiology of hypertension. A small number of patients (2-5%) have an underlying renal or adrenal disease as the cause for their raised blood pressure. In the remainder (95%) however no clear single identifiable cause is found and their condition is labelled 'essential hypertension' (2, 3). Primary mechanism involved in the development of essential hypertension remains unclear, in part due to its multifactorial origin. Probably many interrelated factors contribute to the raised blood pressure in hypertensive patients, and their relative roles may differ between individuals. Among the factors that have been most intensively considered are genetic profiles and high salt intake (3). High BP values have been observed in populations with high salt intakes (4) and treatment strategie
On Harish-Chandra bimodules of rational Cherednik algebras at regular parameter values
Get PDFThis thesis deals with Harish-Chandra bimodules of rational Cherednik algebras Hk at regular
parameter values k, that is those k for which Hk is a simple algebra. Rational Cherednik
algebras can be associated to any re
ection representation of a complex re
ection group .
The second chapter presents a review of some important results regarding rational Cherednik
algebras and their category Ok, which will be frequently used throughout.
The third chapter contains basic results about Harish-Chandra bimodules and the structure
of the category HCk of Harish-Chandra bimodules, many of which are new in the context
of complex re
ection groups but have known analogues for real re
ection groups at integral
parameter values by work of Berest-Etingof-Ginzburg in [BEG03b]. In particular we show that
if k is regular, then HCk is a semisimple tensor category and is equivalent to a tensor-closed
subcategory of modules of the associated Hecke algebra. Using work of I. Losev in [Los11a],
we also deduce that HCk is equivalent as a tensor category to repC (=Nk), the representation
category of a quotient of the complex re
ection group . This extends previous results for the
case of integral k. We manage to obtain some numerical consequences for the presentation of
the Hecke algebra of , which is linked to Hk and Ok via the KZk-functor.
The fourth chapter again is a review of standard results on Morita equivalences between rings
and integral shift functors giving Morita equivalences between rational Cherednik algebras and
their tensor categories of Harish-Chandra bimodules at di erent regular parameter values. The
case of integral parameter values k is discussed brie
y, going back to Berest-Etingof-Ginzburg
in [BEG03b] and Berest-Chalykh in [BC09]. The fth chapter gives a complete description of
Nk and its dependence on k (still for k regular) for the case that is cyclic.
In chapter 6 we deal with nite-dimensional Harish-Chandra bimodules of rational Cherednik
algebras associated to cyclic groups, compute the quiver of that category and derive a criterion
for wildness of HCk in the cyclic case.
Chapter 7 nally extends a classi cation of the structure of HCk as a tensor category for regular
k to nite irreducible Coxeter groups
Spatially-localized time dependent solutions including turbulence and their interactions in 2D Kolmogorov flow
No full textIn 2D Kolmogorov flow in small aspect ratio domains, spatially-localized solutions such as kink, traveling or time-dependent kink-antikink pars coexist. However, the conservation of the flow rate in the y direction strongly restrict combination of localized solutions and their positioning. We find that by adding a homogeneous flow U y their positioning is controlled and each of localized solutions including a spatially-localized chaos is isolated. Numerical results suggest that these isolated solutions can be elements constructing a whole flow
- …
