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A Floer-Theoretic Interpretation of the Polynomial Representation of the Double Affine Hecke Algebra.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	A Floer-Theoretic Interpretation of the Polynomial Representation of the Double Affine Hecke Algebra./
Author:	Reisin-Tzur, Eilon.
Description:	1 online resource (72 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
Contained By:	Dissertations Abstracts International85-03B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798380332811

A Floer-Theoretic Interpretation of the Polynomial Representation of the Double Affine Hecke Algebra.
Reisin-Tzur, Eilon.

A Floer-Theoretic Interpretation of the Polynomial Representation of the Double Affine Hecke Algebra. - 1 online resource (72 pages)

Source: Dissertations Abstracts International, Volume: 85-03, Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2023.

Includes bibliographical references

We construct an isomorphism between the wrapped higher-dimensional Heegaard Floer homology of κ-tuples of cotangent fibers and κ-tuples of conormal bundles of homotopically nontrivial simple closed curves in T ∗Σ with a certain braid skein group, where Σ is a closed oriented surface of genus > 0 and κ is a positive integer. Moreover, we show this produces a (right) module over the surface Hecke algebra associated to Σ. This module structure is shown to be equivalent to the polynomial representation of DAHA in the case where Σ = T 2 and the cotangent fibers and conormal bundles of curves are both parallel copies.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380332811Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Braid skein algebraIndex Terms--Genre/Form:

554714
Electronic books.

A Floer-Theoretic Interpretation of the Polynomial Representation of the Double Affine Hecke Algebra.
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245 1 2 $a A Floer-Theoretic Interpretation of the Polynomial Representation of the Double Affine Hecke Algebra.
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300 $a 1 online resource (72 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
500 $a Advisor: Honda, Ko.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2023.
504 $a Includes bibliographical references
520 $a We construct an isomorphism between the wrapped higher-dimensional Heegaard Floer homology of κ-tuples of cotangent fibers and κ-tuples of conormal bundles of homotopically nontrivial simple closed curves in T ∗Σ with a certain braid skein group, where Σ is a closed oriented surface of genus > 0 and κ is a positive integer. Moreover, we show this produces a (right) module over the surface Hecke algebra associated to Σ. This module structure is shown to be equivalent to the polynomial representation of DAHA in the case where Σ = T 2 and the cotangent fibers and conormal bundles of curves are both parallel copies.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Theoretical mathematics. $3 1180455
653 $a Braid skein algebra
653 $a Hecke algebra
653 $a Geometry
653 $a Heegaard Floer homology
653 $a Topology
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 1180777
773 0 $t Dissertations Abstracts International $g 85-03B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30639493 $z click for full text (PQDT)