Distinction of the Steinberg representation for inner forms of GL(n)

作者：Matringe Nadir^*

来源：Mathematische Zeitschrift, 2017, 287(3-4): 881-895.

DOI：10.1007/s00209-017-1849-4

Let F be a non archimedean local field of characteristic not 2. Let D be a division algebra of dimension over its center F, and E a quadratic extension of F. If m is a positive integer, to a character of , one can attach the Steinberg representation of . Let H be the group GL(m, D), we prove that is H-distinguished if and only if is the quadratic character , where is the character of with kernel the norms of . We also get multiplicity one for the space of invariant linear forms.

• 出版日期2017-12