%0 Journal Article %T Non-cuspidality outside the middle degree of l-adic cohomology of the Lubin-Tate tower %A Yoichi Mieda %J Mathematics %D 2008 %I arXiv %X In this article, we consider the representations of the general linear group over a non-archimedean local field obtained from the vanishing cycle cohomology of the Lubin-Tate tower. We give an easy and direct proof of the fact that no supercuspidal representation appears as a subquotient of such representations unless they are obtained from the cohomology of the middle degree. Our proof is purely local and does not require Shimura varieties. %U http://arxiv.org/abs/0806.0697v1