Spherical and Whittaker functions via DAHA I
Identifieur interne : 000131 ( Main/Exploration ); précédent : 000130; suivant : 000132Spherical and Whittaker functions via DAHA I
Auteurs : Ivan Cherednik [États-Unis] ; Xiaoguang Ma [Canada]Source :
- Selecta Mathematica [ 1022-1824 ] ; 2013-08-01.
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Abstract
Abstract: This paper begins with an exposition of the classical $$p$$ -adic theory of the Macdonald, Matsumoto, and Whittaker functions aimed at the affine generalizations. The major directions are as follows: (1) extending the theory of DAHA to arbitrary levels and (2) the affine Satake map and Hall functions via DAHA. The key result is the proportionality of the two different formulas for the affine symmetrizer, the Satake-type formula and that based on the polynomial representation of DAHA. The latter approach results in two important formulas for the affine symmetrizer generalizing the relations between the Kac–Moody characters and Demazure characters.
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DOI: 10.1007/s00029-012-0110-6
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Math. New Ser.</title><idno type="ISSN">1022-1824</idno><idno type="eISSN">1420-9020</idno><imprint><publisher>Springer Basel</publisher><pubPlace>Basel</pubPlace><date type="published" when="2013-08-01">2013-08-01</date><biblScope unit="volume">19</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="737">737</biblScope><biblScope unit="page" to="817">817</biblScope></imprint><idno type="ISSN">1022-1824</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1022-1824</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>$$p$$ -adic spherical functions</term><term>Hall functions</term><term>Hecke algebras</term><term>Macdonald polynomials</term><term>Matsumoto functions</term><term>Satake isomorphism</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: This paper begins with an exposition of the classical $$p$$ -adic theory of the Macdonald, Matsumoto, and Whittaker functions aimed at the affine generalizations. The major directions are as follows: (1) extending the theory of DAHA to arbitrary levels and (2) the affine Satake map and Hall functions via DAHA. The key result is the proportionality of the two different formulas for the affine symmetrizer, the Satake-type formula and that based on the polynomial representation of DAHA. The latter approach results in two important formulas for the affine symmetrizer generalizing the relations between the Kac–Moody characters and Demazure characters.</div></front></TEI><affiliations><list><country><li>Canada</li><li>États-Unis</li></country><region><li>Caroline du Nord</li></region></list><tree><country name="États-Unis"><region name="Caroline du Nord"><name sortKey="Cherednik, Ivan" sort="Cherednik, Ivan" uniqKey="Cherednik I" first="Ivan" last="Cherednik">Ivan Cherednik</name></region><name sortKey="Cherednik, Ivan" sort="Cherednik, Ivan" uniqKey="Cherednik I" first="Ivan" last="Cherednik">Ivan Cherednik</name></country><country name="Canada"><noRegion><name sortKey="Ma, Xiaoguang" sort="Ma, Xiaoguang" uniqKey="Ma X" first="Xiaoguang" last="Ma">Xiaoguang Ma</name></noRegion><name sortKey="Ma, Xiaoguang" sort="Ma, Xiaoguang" uniqKey="Ma X" first="Xiaoguang" last="Ma">Xiaoguang Ma</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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