@prefix vivo: . @prefix edm: . @prefix dcterms: . @prefix dc: . @prefix skos: . @prefix ns0: . vivo:departmentOrSchool "Non UBC"@en ; edm:dataProvider "DSpace"@en ; dcterms:creator "Muthiah, Dinakar"@en ; dcterms:issued "2017-02-05T20:21:03"@en, "2016-07-28T13:29"@en ; dcterms:description """Recently, Braverman, Kazhdan, and Patnaik have constructed Iwahori-Hecke algebras for p-adic loop groups. Unsurprisingly, the resulting algebra is a variation on Cherednik's DAHA. The p-adic construction also comes with a basis (the double-coset basis) consisting of indicator functions of Iwahori double cosets. Braverman, Kazhdan, and Patnaik also proposed a (double affine) Bruhat preorder on the set of double cosets, which they conjectured to be a poset. I will describe a combinatorial presentation of the double-coset basis and also an alternative way to develop the double affine Bruhat order that is closely related to this combinatorics; from this perspective the order is manifestly a poset. One new feature is a length function that is compatible with the order. I will also discuss joint work with Daniel Orr, where we give a positive answer to a question raised in a previous paper: we prove that the length function can be specialized to take values in the integers. This proves finiteness of chains in the double-affine Bruhat order, and it gives an expected dimension formula for (yet to be defined) transversal slices in the double affine flag variety. If time remains, I will discuss how these results are stepping stones for developing Kazhdan-Lusztig theory in this setting and a number of further open questions."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/60433?expand=metadata"@en ; dcterms:extent "50 minutes"@en ; dc:format "video/mp4"@en ; skos:note ""@en, "Author affiliation: University of Alberta"@en ; edm:isShownAt "10.14288/1.0340925"@en ; dcterms:language "eng"@en ; ns0:peerReviewStatus "Unreviewed"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ; ns0:scholarLevel "Postdoctoral"@en ; dcterms:isPartOf "BIRS Workshop Lecture Videos (Banff, Alta)"@en ; dcterms:subject "Mathematics"@en, "Number theory"@en, "Quantum theory"@en ; dcterms:title "Double affine Bruhat order and Iwahori-Hecke algebras for $p$-adic loop groups"@en ; dcterms:type "Moving Image"@en ; ns0:identifierURI "http://hdl.handle.net/2429/60433"@en .