114 research outputs found
Structures paraboliques transverses et opérateurs BGG transverses
No full textManifolds endowed with a parabolic geometry in the sense of Cartan come with natural sequences of differential operators and their analysis provide the so called (curved) BGG sequence of Čap, Slovák and Souček. The sequences involved do not form an elliptic complex in the sense of Atiyah but enjoy similar properties. The proper framework to study these operators is the filtered calculus associated to the natural filtration of the tangent bundle induced by the parabolic geometry. Such analysis was carried over by Dave and Haller in a very general setting. In this article we use their methods associated with the transversal index theory for filtered manifolds developped by the author in a previous paper to derive curved BGG sequences for foliated manifolds with transverse parabolic geometry
Transverse Parabolic Structures and Transverse BGG Sequences
No full textManifolds endowed with a parabolic geometry in the sense of Cartan come with natural sequences of differential operators and their analysis provide the so called (curved) BGG sequence of Cap, Slovak and Soucek. The sequences involved do not form an elliptic complex in the sense of Atiyah but enjoy similar properties. The proper framework to study these operators is the filtered calculus associated to the natural filtration of the tangent bundle induced by the parabolic geometry. Such analysis was carried over by Dave and Haller in a very general setting. In this article we use their methods associated with the transversal index theory for filtered manifolds developed by the author in a previous paper to derive curved BGG sequences for foliated manifolds with transverse parabolic geometry.Keywords: Bernstein-Gelfand-Gelfand operators, foliation, parabolic geometry, pseudodifferential calculus, analysis on Lie groups.MSC: 58H05, 58A10; 58A14, 58A30, 58J22
Curved Casimir Operators and the BGG Machinery
No full textWe prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the resulting invariant operators and compute their action on various special types of natural bundles. As a first application, we give a very general construction of splitting operators for parabolic geometries. Then we discuss the curved Casimir operators on differential forms with values in a tractor bundle, which nicely relates to the machinery of BGG sequences. This also gives a nice interpretation of the resolution of a finite dimensional representation by (spaces of smooth vectors in) principal series representations provided by a BGG sequence.This paper is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson. The idea to study the Casimir operator on tractor bundle valued forms grew out of questions by M. Cowling and by P. Julg, who conjectured Corollary 1 for the case of the trivial representation. We are very grateful to them for drawing our attention to this problem. Our thanks also go to the anonymous referees for helpful suggestions and corrections. Most of the work was done during meetings of authors at the Erwin Schr¨odinger Institute for Mathematical Physics in Vienna. First author supported by project P19500–N13 of the Fonds zur F¨orderung der wissenschaftlichen Forschung (FWF). The second author thanks the grant GACR Nr. 201/05/2117 and the institutional grant MSM 0021620839 for their support
Curved Casimir Operators and the BGG Machinery
No full textWe prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the resulting invariant operators and compute their action on various special types of natural bundles. As a first application, we give a very general construction of splitting operators for parabolic geometries. Then we discuss the curved Casimir operators on differential forms with values in a tractor bundle, which nicely relates to the machinery of BGG sequences. This also gives a nice interpretation of the resolution of a finite dimensional representation by (spaces of smooth vectors in) principal series representations provided by a BGG sequence.This paper is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson. The idea to study the Casimir operator on tractor bundle valued forms grew out of questions by M. Cowling and by P. Julg, who conjectured Corollary 1 for the case of the trivial representation. We are very grateful to them for drawing our attention to this problem. Our thanks also go to the anonymous referees for helpful suggestions and corrections. Most of the work was done during meetings of authors at the Erwin Schr¨odinger Institute for Mathematical Physics in Vienna. First author supported by project P19500–N13 of the Fonds zur F¨orderung der wissenschaftlichen Forschung (FWF). The second author thanks the grant GACR Nr. 201/05/2117 and the institutional grant MSM 0021620839 for their support
Bank capital regulation, the lending channel and business cycles
No full textThis paper develops a Dynamic Stochastic General Equilibrium (DSGE) model to study how the instability of the banking sector can amplify and propagate business cycles. The model builds on Bernanke, Gertler and Gilchrist (BGG) (1999), who consider credit demand friction due to agency cost, but it deviates from BGG in that financial intermediaries have to share aggregate risk with entrepreneurs, and therefore bear uncertainty in their loan portfolios. Unexpected aggregate shocks will drive loan default rate away from expected, and have an impact on both firm and bank's balance sheet via the financial contract. Low bank capital position can create strong credit supply contraction, and have a significant effect on business cycle dynamics. --Bank capital regulation,banking instability,financial friction,business cycle
Sex-specific effects of in utero and adult tobacco smoke exposure.
No full textTobacco smoke has harmful effects on a multiorgan level. Exposure to smoke, whether in utero or environmental, significantly increases susceptibility. This susceptibility has been identified to be divergent between males and females. However, there remains a distinct lack of thorough research into the relationship between sex and exposure to tobacco. Females tend to generate a more significant response than males during adulthood exposure. The intrauterine environment is meticulously controlled, and exposure to tobacco presents a significant factor that contributes to poor health outcomes and susceptibility later in life. Analysis of these effects in relation to the sex of the offspring is yet to be holistically reviewed and summarized. In this review, we will delineate the time-dependent relationship between tobacco smoke exposure and sex-specific disease susceptibility. We further outline possible biological mechanisms that may contribute to the identified pattern
Do we really need to keep redesigning β<inf>2</inf>-agonists for the management of asthma?
No full text© 2015 Bentham Science Publishers. There is an enormous drive to refine therapeutic designs and delivery systems, but in this review we ask if this is always the right direction? We choose to play devil's advocate, and argue that refining drug design is not always needed, and what is actually needed is a greater understanding of the biology of the disease. Here we focus on asthma and the β2-agonist group of bronchodilators as an example of how a class of therapeutic has been developed and continues to be developmentally refined. In this review, we define viralinduced exacerbations as the greatest cause of lung attacks and the most crucial time β2-agonist therapy is needed. We explore the reasons why β2-agonist therapy fails in patients with rhinovirus-induced exacerbations, and explain why further “engineered” β2-agonist therapies are likely to continue to fail in this subset of asthmatic population. We justify our perspective by returning to the biology that underlies the cause of disease and highlight the need for “more research” into alternative therapies for this population of asthmatic patients
Sexual dimorphism in chronic respiratory diseases.
No full textSex differences in susceptibility, severity, and progression are prevalent for various diseases in multiple organ systems. This phenomenon is particularly apparent in respiratory diseases. Asthma demonstrates an age-dependent pattern of sexual dimorphism. However, marked differences between males and females exist in other pervasive conditions such as chronic obstructive pulmonary disease (COPD) and lung cancer. The sex hormones estrogen and testosterone are commonly considered the primary factors causing sexual dimorphism in disease. However, how they contribute to differences in disease onset between males and females remains undefined. The sex chromosomes are an under-investigated fundamental form of sexual dimorphism. Recent studies highlight key X and Y-chromosome-linked genes that regulate vital cell processes and can contribute to disease-relevant mechanisms. This review summarises patterns of sex differences in asthma, COPD and lung cancer, highlighting physiological mechanisms causing the observed dimorphism. We also describe the role of the sex hormones and present candidate genes on the sex chromosomes as potential factors contributing to sexual dimorphism in disease
Kazhdan-Lusztig theory of super type D and quantum symmetric pairs
No full textWe reformulate the Kazhdan-Lusztig theory for the BGG category
O
\mathcal {O}
of Lie algebras of type D via the theory of canonical bases arising from quantum symmetric pairs initiated by Weiqiang Wang and the author. This is further applied to formulate and establish for the first time the Kazhdan-Lusztig theory for the BGG category
O
\mathcal {O}
of the ortho-symplectic Lie superalgebra
o
s
p
(
2
m
|
2
n
)
\mathfrak {osp}(2m|2n)
.</p
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