{"id":1297,"date":"2018-11-14T20:49:33","date_gmt":"2018-11-14T18:49:33","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=1297"},"modified":"2018-11-22T12:43:43","modified_gmt":"2018-11-22T10:43:43","slug":"colloquium-tuesday-november-20-2018-speaker-eyal-kaplan-bar-ilan-title-doubling-constructions-and-applications","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=1297","title":{"rendered":"Colloquium: Tuesday, November 20, 2018. Speaker: Eyal Kaplan (Bar-Ilan). Title: &#8220;Doubling constructions and applications&#8221;."},"content":{"rendered":"<p>Integral representations are a fundamental tool in the study of automorphic L functions.<\/p>\n<div class=\"WordSection1\">\n<p class=\"xmsonormal\"><span style=\"font-size: 12pt; font-family: 'Arial',sans-serif; color: #222222;\">One of these constructions, developed by Piatetski-Shapiro and Rallis in the late 80s, <\/span><\/p>\n<p class=\"xmsonormal\"><span style=\"font-size: 12pt; font-family: 'Arial',sans-serif; color: #222222;\">produced the standard L function for any cuspidal representation of a classical group, <\/span><\/p>\n<p class=\"xmsonormal\"><span style=\"font-size: 12pt; font-family: 'Arial',sans-serif; color: #222222;\">or its rank-1 twist. In a recent collaboration with Cai, Friedberg and Ginzburg, we extended <\/span><\/p>\n<p class=\"xmsonormal\"><span style=\"font-size: 12pt; font-family: 'Arial',sans-serif; color: #222222;\">the doubling method to produce the tensor product L function of G X GL(k), where G <\/span><\/p>\n<p class=\"xmsonormal\"><span style=\"font-size: 12pt; font-family: 'Arial',sans-serif; color: #222222;\">is a classical group and k is arbitrary. I will discuss recent applications of this construction <\/span><\/p>\n<p class=\"xmsonormal\"><span style=\"font-size: 12pt; font-family: 'Arial',sans-serif; color: #222222;\">to the study of automorphic forms on classical groups as well as on covering groups.<\/span><span style=\"font-size: 12pt; font-family: 'Times New Roman',serif; color: #212121;\">\u00a0<\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Integral representations are a fundamental tool in the study of automorphic L functions. One of these constructions, developed by Piatetski-Shapiro and Rallis in the late 80s, produced the standard L function for any cuspidal representation of a classical group, or&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=1297\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-1297","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1297","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1297"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1297\/revisions"}],"predecessor-version":[{"id":1298,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1297\/revisions\/1298"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1297"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1297"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}