The divine sympathy: an essay on kenotic Christology

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On the variety of Lagrangian subalgebras, I

We study subalgebras of a semi-simple Lie algebra which are Lagrangian with respect to the imaginary part of the Killing form. We show that the variety L of Lagrangian subalgebras carries a natural Poisson structure Π. We determine the irreducible components of L, and we show that each irreducible component is a smooth fiber bundle over a generalized flag variety, and that the fiber is the product of the set of real points of a De Concini-Procesi compactification and a connected component of a real orthogonal group. We study some properties of the Poisson structure Π and show that L contains many interesting Poisson submanifolds. © 2001 Éditions scientifiques et médicales Elsevier SAS.postprin

Transverse measures, the modular class and a cohomology pairing for Lie algebroids

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Allogeneic hematopoietic cell transplantation as curative therapy for patients with non-Hodgkin lymphoma: Increasingly successful application to older patients

AbstractNon-Hodgkin lymphoma (NHL) constitutes a collection of lymphoproliferative disorders with widely varying biological, histological, and clinical features. For the B cell NHLs, great progress has been made due to the addition of monoclonal antibodies and, more recently, other novel agents including B cell receptor signaling inhibitors, immunomodulatory agents, and proteasome inhibitors. Autologous hematopoietic cell transplantation (auto-HCT) offers the promise of cure or prolonged remission in some NHL patients. For some patients, however, auto-HCT may never be a viable option, whereas in others, the disease may progress despite auto-HCT. In those settings, allogeneic HCT (allo-HCT) offers the potential for cure. Over the past 10 to 15 years, considerable progress has been made in the implementation of allo-HCT, such that this approach now is a highly effective therapy for patients up to (and even beyond) age 75 years. Recent advances in conventional lymphoma therapy, peritransplantation supportive care, patient selection, and donor selection (including the use of alternative hematopoietic cell donors), has allowed broader application of allo-HCT to patients with NHL. As a result, an ever-increasing number of NHL patients over age 60 to 65 years stand to benefit from allo-HCT. In this review, we present data in support of the use of allo-HCT for patients with diffuse large B cell lymphoma, follicular lymphoma, and mantle cell lymphoma. These histologies account for a large majority of allo-HCTs performed for patients over age 60 in the United States. Where possible, we highlight available data in older patients. This body of literature strongly supports the concept that allo-HCT should be offered to fit patients well beyond age 65 and, accordingly, that this treatment should be covered by their insurance carriers

Clinicopathologic consensus study of gray zone lymphoma with features intermediate between DLBCL and classical HL

Gray zone lymphoma (GZL) is described as sharing features with classical Hodgkin lymphoma (cHL) and diffuse large B-cell lymphoma (DLBCL). However, there remains complexity in establishing diagnosis, delineating prognosis, and determining optimum therapy. Sixty-eight cases diagnosed as GZL across 15 North American academic centers were evaluated by central pathology review to achieve consensus. Of these, only 26 (38%) were confirmed as GZL. Morphology was critical to GZL consensus diagnosis (eg, tumor cell richness); immunohistochemistry showed universal B-cell derivation, frequent CD30 expression, and rare Epstein-Barr virus (EBV) positivity (CD20(+), 83%; PAX5(+), 100%; BCL6(+), 20%; MUM1(+), 100%; CD30(+), 92%; EBV(+), 4%). Forty-two cases were reclassified: nodular sclerosis (NS) cHL, n = 27 (including n = 10 NS grade 2); lymphocyte predominant HL, n = 4; DLBCL, n = 4; EBV(+) DLBCL, n = 3; primary mediastinal large BCL n = 2; lymphocyte-rich cHL and BCL-not otherwise specified, n = 1 each. GZL consensus-confirmed vs reclassified cases, respectively, more often had mediastinal disease (69% vs 41%; P = .038) and less likely more than 1 extranodal site (0% vs 25%; P = .019). With a 44-month median follow-up, 3-year progression-free survival (PFS) and overall survival for patients with confirmed GZL were 39% and 95%, respectively, vs 58% and 85%, respectively, for reclassified cases (P = .19 and P = .15, respectively). Interestingly, NS grade 2 reclassified patients had similar PFS as GZL consensus-confirmed cases. For prognostication of GZL cases, hypoalbuminemia was a negative factor (3-year PFS, 12% vs 64%; P = .01), whereas frontline cyclophosphamide, doxorubicin, vincristine, and prednisone +/- rituximab (CHOP+/-R) was associated with improved 3-year PFS (70% vs 20%; P = .03); both factors remained significant on multivariate analysis. Altogether, accurate diagnosis of GZL remains challenging, and improved therapeutic strategies are needed

Modular classes of Poisson-Nijenhuis Lie algebroids

The modular vector field of a Poisson-Nijenhuis Lie algebroid $A$ is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian $A$-vector fields. This hierarchy covers an integrable hierarchy on the base manifold, which may not have a Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic

Formal Hecke algebras and algebraic oriented cohomology theories

In the present paper we generalize the construction of the nil Hecke ring of Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's K_0, connective K-theory, elliptic cohomology, and algebraic cobordism. The resulting object, which we call a formal (affine) Demazure algebra, is parameterized by a one-dimensional commutative formal group law and has the following important property: specialization to the additive and multiplicative periodic formal group laws yields completions of the nil Hecke and the 0-Hecke rings respectively. We also introduce a deformed version of the formal (affine) Demazure algebra, which we call a formal (affine) Hecke algebra. We show that the specialization of the formal (affine) Hecke algebra to the additive and multiplicative periodic formal group laws gives completions of the degenerate (affine) Hecke algebra and the usual (affine) Hecke algebra respectively. We show that all formal affine Demazure algebras (and all formal affine Hecke algebras) become isomorphic over certain coefficient rings, proving an analogue of a result of Lusztig.Comment: 28 pages. v2: Some results strengthened and references added. v3: Minor corrections, section numbering changed to match published version. v4: Sign errors in Proposition 6.8(d) corrected. This version incorporates an erratum to the published versio

On localization in holomorphic equivariant cohomology

We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the exposition. v4: final version to appear in Centr. Eur. J. Mat

Weak splittings of quotients of Drinfeld and Heisenberg doubles

We investigate the fine structure of the simplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson-Dirac submanifolds of the torus orbits of the doubles. The results have a wide range of applications to many families of real and complex Poisson structures on flag varieties. Their torus orbits of leaves recover important families of varieties such as the open Richardson varieties.Comment: 20 pages, AMS Late