Conductors and newforms for U(1,1)

Let $F$ be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms for $U(1,1)(F)$, building on previous work on $SL_2(F)$. This theory is analogous to the results of Casselman for $GL_2(F)$ and Jacquet, Piatetski-Shapiro, and Shalika for $GL_n(F)$. To a representation $\pi$ of $U(1,1)(F)$, we attach an integer $c(\pi)$ called the conductor of $\pi$, which depends only on the $L$-packet $\Pi$ containing $\pi$. A newform is a vector in $\pi$ which is essentially fixed by a congruence subgroup of level $c(\pi)$. We show that our newforms are always test vectors for some standard Whittaker functionals, and, in doing so, we give various explicit formulae for newforms.Comment: 25 page

Patients as Consumers: Making the Health Care System Our Own. 9th Annual Herbert Lourie Memorial Lecture on Health Policy.

I ask you to think about our health care system. Think beyond the issues that are in front of us today: the anxiety we have about managed care, obtaining our own health care and paying for it, the survival of Medicare, and the unpredictable impact of government regulations. Think about our *health*, what we want from our health care system, what we're spending all this money for, and what we care about for ourselves and for our families. The challenge we face in the next five, ten, or fifteen years is to place the American health care system under the control of the people who pay for it, who receive the care, and who care the most about the health of the people in our communities.

Lifting representations of finite reductive groups II: Explicit conorms

Let $k$ be a field, $\tilde{G}$ a connected reductive $k$-quasisplit group, $\Gamma$ a finite group that acts on $\tilde{G}$ via $k$-automorphisms satisfying a quasi-semisimplicity condition, and $G$ the connected part of the group of $\Gamma$-fixed points of $\tilde{G}$, also assumed $k$-quasisplit. In an earlier work, the authors constructed a canonical map $\hat{\mathcal{N}}$ from the set of stable semisimple conjugacy classes in the dual $G^*(k)$ to the set of such classes in $\tilde{G}^*(k)$. We describe several situations where $\hat{\mathcal{N}}$ can be refined to an explicit function on points, or where it factors through such a function