Proceedings Mathematical Sciences | |
On Counting Twists of a Character Appearing in its Associated Weil Representation | |
K Vishnu Namboothiri1  | |
[1] Department of Mathematics and Statistics, University of Hyderabad, Hyderabad 00 0, India$$ | |
关键词: Nonarchimedian local field; irreducible; admissible representation of $GL(2; F); in$-factor of a character; Weil representation; number of characters appearing in its restriction.; | |
DOI : | |
学科分类:数学(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
Consider an irreducible, admissible representation 𜋠of $GL(2,F)$ whose restriction to $GL(2,F)^+$ breaks up as a sum of two irreducible representations $ðœ‹_+ +ðœ‹_-$. If $ðœ‹=r_θ$, the Weil representation of $GL(2,F)$ attached to a character θ of $K^∗$ does not factor through the norm map from ð¾ to ð¹, then $ðœ’in widehat{K^∗}$ with $(ðœ’cdot p^{θ^{-1}})|F^∗=𜔠K/F$ occurs in $r_{θ+}$ if and only if $in(θðœ’^{-1},psi_0)=in(overline{θ}ðœ’^{-1},psi_0)=1$ and in $r_{θ−}$ if and only if both the epsilon factors are $-1$. But given a conductor ð‘›, can we say precisely how many such 𜒠will appear in ðœ‹? We calculate the number of such characters at each given conductor ð‘› in this work.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO201912040506925ZK.pdf | 296KB | download |