Matching of orbital integrals (transfer) and Roche Hecke algebra isomorphisms

Let $F$ be a non-Archimedan local field, $G$ a connected reductive group defined and split over $F$, and $T$ a maximal $F$-split torus in $G$. Let $\chi_0$ be a depth zero character of the maximal compact subgroup $\mathcal{T}$ of $T(F)$. It gives by inflation a character $\rho$ of an Iwahori subgroup $\mathcal{I}$ of $G(F)$ containing $\mathcal{T}$. From Roche, $\chi_0$ defines a split endoscopic group $G'$ of $G$, and there is an injective morphism of ${\Bbb C}$-algebras $\mathcal{H}(G(F),\rho) \rightarrow \mathcal{H}(G'(F),1_{\mathcal{I}'})$ where $\mathcal{H}(G(F),\rho)$ is the Hecke algebra of compactly supported $\rho^{-1}$-spherical functions on $G(F)$ and $\mathcal{I}'$ is an Iwahori subgroup of $G'(F)$. This morphism restricts to an injective morphism $\zeta: \mathcal{Z}(G(F),\rho)\rightarrow \mathcal{Z}(G'(F),1_{\mathcal{I}'})$ between the centers of the Hecke algebras. We prove here that a certain linear combination of morphisms analogous to $\zeta$ realizes the transfer (matching of strongly $G$-regular semisimple orbital integrals). If ${\rm char}(F)=p>0$, our result is unconditional only if $p$ is large enough.Comment: 82 page

Effects of heme oxygenase system on inflammation, oxidative stress, insulin signaling and tissue injury in liver, heart, kidney and pancreas in obese, diabetic and hypertensive rats

Tissue injury and metabolic dysfunction are salient features of obesity, diabetes, and hypertension. Inflammation and oxidative stress are considered key players behind this altered tissue homeostasis that drastically affect several vital organs including liver, heart, kidney and pancreas resulting in the development of hepatic steatosis, cardiomyopathy, nephropathy, pancreatic insulitis and abnormal glucose metabolism. Despite significant advancement in pharmaceutical interventions, the desired efficacy to manage these conditions is still lacking. In these situations, cytoprotective and functional attributes of the heme oxygenase (HO) system can be used as an alternative management tool. Although, the HO system is cytoprotective, its role in tissue injury and dysfunction in obesity, diabetes, and hypertension is not completely clear. To explore the importance of upregulating HO in these conditions, HO is induced through hemin in the rat models of obesity, diabetes and hypertension. My thesis work show that HO upregulation reduced the inflammation and oxidative stress-induced tissue injury in liver, heart, kidney, and pancreas through reduction of proinflammatory M1 macrophage marker (ED1) expression, cytokines (TNF-α, IL-1β, IL-6), oxidative-markers (8-isoprostane, ET-1) and profibrotic/extracellular matrix proteins (TGF-β, collagen-IV, fibronectin) and enhancement of the anti-inflammatory M2-macrophage markers (ED2, CD206, CD36, CD14), adiponectin and total-antioxidant capacity. HO upregulation improved glucose metabolism through potentiation of insulin signalling components (IRS-1, IRS-2, PI3K, GLUT4), reduced hyperglycemia, and enhanced several markers implicated in pancreatic repair and/or regeneration (c-Kit, Sca-1, Oct3/4, Pax2, β-catenin, Islet-1, Nkx6.1 and GLUT2). Collectively, the data from my thesis suggested the multifaceted cytoprotective mechanisms of the HO system against increasing tissue injury and metabolic dysfunction during obesity, diabetes and hypertension. Thus, HO upregulation through hemin may be part of therapeutic management strategies against tissue injury and metabolic dysfunction in obesity, diabetes and hypertension in the future

Andaman mangrove sediments: source of nutrients and sink of heavy metals

156-166Andaman Islands (AI) of India is a biodiversity hotspot of mangroves but biogeochemical dynamics of AI is less understood. We collected sediment samples from four AI mangrove sites and one site without mangroves for nutrients and trace metal analysis. Samples were collected from each site at the inlet of seawater (Zone A) and the other 500 m into the mangrove creek (Zone B). Nutrients (sulphate, ammonium, nitrite and nitrate) level, organic matter (OM) and carbon content were higher at Zone B of mangrove ecosystem due to the higher OM content from mangrove leaf litter decomposition and microbial degradation. Metal (Pb & Cd) content of zones with and without mangroves were similar and Igeo values indicated moderate contamination of mangrove zones of AI due to lack of anthropogenic pollution. Our results suggest mangrove ecosystems of AI are uncontaminated from heavy metals and are source of nutrients to the oligotrophic coastal ecosystems of Andaman Sea