Intertwining of simple characters in GL(n)

Let $F$ be a non-Archimedean local field and let $G$ be the general linear group $G = \text{\rm GL}_n(F)$. Let $\theta_1$, $\theta_2$ be simple characters in $G$. We show that $\theta_1$ intertwines with $\theta_2$ if and only if $\theta_1$ is endo-equivalent to $\theta_2$. We also show that any simple character in $G$ is a $G$-type.Comment: 7 page

Tame multiplicity and conductor for local Galois representations

Let $F$ be a non-Archimedean locally compact field of residual characteristic $p$. Let $\sigma$ be an irreducible smooth representation of the absolute Weil group \Cal W_F of $F$ and \sw(\sigma) the Swan exponent of $\sigma$. Assume \sw(\sigma) \ge1. Let \Cal I_F be the inertia subgroup of \Cal W_F and \Cal P_F the wild inertia subgroup. There is an essentially unique, finite, cyclic group $\varSigma$, of order prime to $p$, so that \sigma(\Cal I_F) = \sigma(\Cal P_F)\varSigma. In response to a query of Mark Reeder, we show that the multiplicity in $\sigma$ of any character of $\varSigma$ is bounded by \sw(\sigma).Comment: Revised version with further detai

Langlands parameters for epipelagic representations of GLn\text{\rm GL}_n

Let $F$ be a non-Archimedean local field. An irreducible cuspidal representation of $\text{\rm GL}_n(F)$ is epipelagic if its Swan conductor equals 1. We give a full and explicit description of the Langlands parameters of such representations.Comment: 25 page

Cycles in the chamber homology of GL(3)

Let F be a nonarchimedean local field and let GL(N) = GL(N,F). We prove the existence of parahoric types for GL(N). We construct representative cycles in all the homology classes of the chamber homology of GL(3).Comment: 45 pages. v3: minor correction

Status of linear boundary-layer stability and the e to the nth method, with emphasis on swept-wing applications

The-state-of-the-art for the application of linear stability theory and the e to the nth power method for transition prediction and laminar flow control design are summarized, with analyses of previously published low disturbance, swept wing data presented. For any set of transition data with similar stream distrubance levels and spectra, the e to the nth power method for estimating the beginning of transition works reasonably well; however, the value of n can vary significantly, depending upon variations in disturbance field or receptivity. Where disturbance levels are high, the values of n are appreciably below the usual average value of 9 to 10 obtained for relatively low disturbance levels. It is recommended that the design of laminar flow control systems be based on conservative estimates of n and that, in considering the values of n obtained from different analytical approaches or investigations, the designer explore the various assumptions which entered into the analyses

Semisimple types for p -adic classical groups

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