The first pro-pp-Iwahori cohomology of mod-pp principal series for pp-adic GLn\textrm{GL}_n

Let $p\geq 3$ be a prime number and $F$ a $p$-adic field. Let $I_1$ denote the pro-$p$-Iwahori subgroup of $\textrm{GL}_n(F)$, and $\mathcal{H}$ the pro-$p$-Iwahori--Hecke algebra of $\textrm{GL}_n(F)$ with respect to $I_1$ (over a coefficient field of characteristic $p$). We compute the structure of $\textrm{H}^1(I_1,\pi)$ as an $\mathcal{H}$-module, where $\pi$ is a mod-$p$ principal series representation of $\textrm{GL}_n(F)$. We also give some partial results about the structure of $\textrm{H}^1(I_1,\pi)$ for a general split reductive group with irreducible root system.Comment: 39 pages. Minor changes following referee report. To appear in Transactions of the AM

Hecke module structure on first and top pro-pp-Iwahori cohomology

Let $p\geq 5$ be a prime number, $G$ a split connected reductive group defined over a $p$-adic field, and $I_1$ a choice of pro-$p$-Iwahori subgroup. Let $C$ be an algebraically closed field of characteristic $p$ and $\mathcal{H}$ the pro-$p$-Iwahori--Hecke algebra over $C$ associated to $I_1$. In this note, we compute the action of $\mathcal{H}$ on $\textrm{H}^1(I_1,C)$ and $\textrm{H}^{\textrm{top}}(I_1,C)$ when the root system of $G$ is irreducible. We also give some partial results in the general case.Comment: 17 pages. Added result about Poincare duality along with other minor changes. To appear in Acta Arithmetic

Magnetostriction of a Superconductor: -Results from the Critical-State Model

In many cases, the critical-state theory can be treated as a suffi ciently accurate approximation for the modelling of the magnetic properties of superconductors. In the present work, the magnetostrictive hysteresis is computed for a quite general case of the modified Kim-Anderson model. The results obtained reproduce many features of the giant magnetostriction (butterfly-shaped curves) reported in the literature for measurements made on single-crystal samples of the high-temperature superconductor $Bi_2Sr_2CaCu_2O_8$. It is shown that addition of a contribution to the magnetostriction in the superconducting state which is of similar origin as in the normal state, offers a broader phenomenological interpretation of the complex magnetostriction hysteresis found in such heavy-fermion compounds as $UPt_3$, $URu_2Si_2$ or $UBe_{13}$.Comment: 9 LaTeX pages, 4 Postscript figures, WWW version available at http://is.dal.ca/~zkoziol/super.htm

Banking Regulation and Financial Accelerators: A One-Period Model with Unlimited Liability

In this paper, we analyze the consequences of bank regulation on the size of the real sector. In particular, we address the question whether exogenous shocks on the return-risk characteristics of the technology and on the equity of the real sector are intensified or damped by a value-at-risk constraint on the credit portfolio of a bank. We consider a one-period model with three risk-averse agents, an investor, a bank, and a firm. The size of the markets for deposits and loans, their prices and the size of the real sector are endogenous. We find that stricter regulation results in higher loan rates, lower deposit rates, and lower activity in the real sector. A negative shock on the return-risk position or on the risk buffer of the real sector reduces the activities in the economy. Surprisingly, the sensitivity of the real sector's activities on negative shocks is smaller for a regulated financial sector than for a non-regulated one. Therefore, in our economy, imperfections in the financial sector do not result in procyclical or acceleration effects