Kirillov Theory for Gl2( ) Where Is a Division Algebra over a Non-archimedean Local Field
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ON THE RESTRICTION TO D∗ ×D∗ OF REPRESENTATIONS OF p-ADIC GL2(D)
Let D be a division algebra for a non-Archimedean local field. Given an irreducible representation π of GL2(D), we describe its restriction to the diagonal subgroup D∗ × D∗. The description is in terms of the structure of the twisted Jacquet module of the representation π. The proof involves Kirillov theory that we have developed earlier in joint work with Dipendra Prasad. The main result on re...
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Hensel [K. Hensel, Deutsch. Math. Verein, {6} (1897), 83-88.] discovered the $p$-adic number as a number theoretical analogue of power series in complex analysis. Fix a prime number $p$. for any nonzero rational number $x$, there exists a unique integer $n_x inmathbb{Z}$ such that $x = frac{a}{b}p^{n_x}$, where $a$ and $b$ are integers not divisible by $p$. Then $|x...
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Following the work of Harris and Kudla we prove a more general form of a conjecture of Jacquet relating the non-vanishing of a certain period integral to non-vanishing of the central critical value of a certain L-function. As a consequence we deduce certain local results about the existence of GL2(k)-invariant linear forms on irreducible, admissible representations of GL2(K) for K a commutative...
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We use the recent proof of Jacquet’s conjecture due to Harris and Kudla, and the Burger-Sarnak principle to give a proof about the relationship between the existence of trilinear forms on representations of GL2(ku) for a non-Archimedean local field ku and local epsilon factors which was earlier proved only in the odd residue characteristic by this author in [P1]. The same method gives a global ...
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تاریخ انتشار 2000