{"id":{"repo_id":"purdue-thes","oai_identifier":"oai:docs.lib.purdue.edu:open_access_dissertations-2562"},"canonical_url":"https://search.dev.ndltd.org/etd/purdue-thes/oai:docs.lib.purdue.edu:open_access_dissertations-2562","repository":{"repo_id":"purdue-thes","name":"Purdue University","base_url":"https://docs.lib.purdue.edu/do/oai/"},"display":{"title":"SUPERCUSPIDAL REPRESENTATIONS ARISING FROM STABLE VECTORS","abstract":"For a reductive group $G$ over a $p$-adic field $k$, one may grade the associated Lie algebra $\\g$ by an automorphism of order $m$. It has been shown that stable vectors $v\\in\\g_{a}$ arise only when $a$ is coprime to $m$. Given a stable vector $v\\in\\g_{a}$, we construct packets of supercuspidal representations $\\{\\pi_{v,\\rho}\\}$ as well as discrete Langlands parameters $\\varphi_{v}$. Both the parameter and representations are of depth $a/m$. We further show that for a fixed vector, $\\pi_{v,\\rho}$ and $\\varphi_{v}$ satisfy both sides of the formal degree conjecture.","abstract_html":"For a reductive group $G$ over a $p$-adic field $k$, one may grade the associated Lie algebra $\\g$ by an automorphism of order $m$. It has been shown that stable vectors <span class=\"etd-inline-math\">v\\in\\g<sub>a</sub></span> arise only when $a$ is coprime to $m$. Given a stable vector <span class=\"etd-inline-math\">v\\in\\g<sub>a</sub></span>, we construct packets of supercuspidal representations <span class=\"etd-inline-math\">\\{&pi;<sub>v,\\rho</sub>\\}</span> as well as discrete Langlands parameters <span class=\"etd-inline-math\">\\varphi<sub>v</sub></span>. Both the parameter and representations are of depth $a/m$. We further show that for a fixed vector, <span class=\"etd-inline-math\">&pi;<sub>v,\\rho</sub></span> and <span class=\"etd-inline-math\">\\varphi<sub>v</sub></span> satisfy both sides of the formal degree conjecture.","abstract_has_math":true,"creators":["Cox, Britain"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Jiu-Kang Yu","Freydoon Shahidi","Tong Liu","David Goldberg"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-01T08:00:00Z","date_published":"2015-01-01T08:00:00Z","updated_at":"2026-07-24T03:54:38Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://docs.lib.purdue.edu/open_access_dissertations/1346","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jiu-Kang Yu","Freydoon Shahidi","Tong Liu","David Goldberg"]},{"key":"dc:creator","label":"Author","values":["Cox, Britain"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://docs.lib.purdue.edu/open_access_dissertations/1346"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["For a reductive group $G$ over a $p$-adic field $k$, one may grade the associated Lie algebra $\\g$ by an automorphism of order $m$. It has been shown that stable vectors $v\\in\\g_{a}$ arise only when $a$ is coprime to $m$. Given a stable vector $v\\in\\g_{a}$, we construct packets of supercuspidal representations $\\{\\pi_{v,\\rho}\\}$ as well as discrete Langlands parameters $\\varphi_{v}$. Both the parameter and representations are of depth $a/m$. We further show that for a fixed vector, $\\pi_{v,\\rho}$ and $\\varphi_{v}$ satisfy both sides of the formal degree conjecture."]},{"key":"dc:title","label":"Title","values":["SUPERCUSPIDAL REPRESENTATIONS ARISING FROM STABLE VECTORS"]}]}],"canonical_facts":{"dc:contributor":["Jiu-Kang Yu","Freydoon Shahidi","Tong Liu","David Goldberg"],"dc:creator":["Cox, Britain"],"dc:description.abstract":["For a reductive group $G$ over a $p$-adic field $k$, one may grade the associated Lie algebra $\\g$ by an automorphism of order $m$. It has been shown that stable vectors $v\\in\\g_{a}$ arise only when $a$ is coprime to $m$. Given a stable vector $v\\in\\g_{a}$, we construct packets of supercuspidal representations $\\{\\pi_{v,\\rho}\\}$ as well as discrete Langlands parameters $\\varphi_{v}$. Both the parameter and representations are of depth $a/m$. We further show that for a fixed vector, $\\pi_{v,\\rho}$ and $\\varphi_{v}$ satisfy both sides of the formal degree conjecture."],"dc:identifier":["https://docs.lib.purdue.edu/open_access_dissertations/1346"],"dc:title":["SUPERCUSPIDAL REPRESENTATIONS ARISING FROM STABLE VECTORS"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:54:38Z"}