User - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T11:31:41Z http://mathoverflow.net/feeds/user/29422 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/116105/on-the-l-function-of-unique-subrepresentation-of-induced-representation On the L-function of unique subrepresentation of induced representation. unknown (google) 2012-12-11T18:22:42Z 2012-12-13T00:54:01Z <p>In studying the L-functions of induced representation, it is not easily come up with me the papers or books dealing the L-function of irreducible subrepresentation of induced representation, while the L-function of Langlands quotient is already defined. So I want to ask you how to define the L-function of it. </p> <p>To explain this more precisely, let me recall some basic notions of it.</p> <p>Let $F$ be a p-adic field and $G$ be an algebraic group over $F$. (we think $G$ as $GL_n(F)$ ) Let $P=MN$ be a parabolic subgroup of $G$ and $M$ and $N$ are its Levi and unipotent subgroups. If we let $\sigma$ be a irreducible supercuspidal representation of $M$ and extend it to $P$ by acting trivially of $N$, we can think the induced representation $I:=Ind_P ^G \sigma$.</p> <p>Then we know that there is a unique irreducible subrepresentation $Z(\sigma)$ of $I$.</p> <p>My question is this. How are the two standard L-functions $L(s,\sigma)$ and $L(s,Z(\sigma))$ related?</p> <p>Furthermore, if $G$ is not general linear group but unitary group, and $E$ is quadratic extension of $F$, then how is the relationship between $L(s,BC(\sigma))$ and $L(s,BC (Z(\sigma)))$? (here $BC$ is the base change of the representation to quadratic extension field $E$)</p> <p>References for this are greatly welcome!</p> http://mathoverflow.net/questions/115714/rallis-inner-product-on-unitary-group Rallis inner product on unitary group. unknown (google) 2012-12-07T13:44:46Z 2012-12-07T13:44:46Z <p>I am wondering whether the Rallis inner product on unitary group is finished.</p> <p>Espescially, I am considering two cases, that is, both ( U(2) -> U(1) ) case &amp; (U(1) -> U(1) ) case.</p> <p>Are these cases already over? If it is, would you recommend me what paper should I refer?</p> http://mathoverflow.net/questions/116105/on-the-l-function-of-unique-subrepresentation-of-induced-representation Comment by 2012-12-14T04:01:45Z 2012-12-14T04:01:45Z Hi! I reccomend you to refer the article 'The local Langland correspondence' written by Kudla contained in the book 'Motive2' by Jannsen U, Kleiman S L, Serre J P.