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A Floer-Theoretic Interpretation of ...

Reisin-Tzur, Eilon.

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A Floer-Theoretic Interpretation of the Polynomial Representation of the Double Affine Hecke Algebra./
作者:	Reisin-Tzur, Eilon.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
面頁冊數:	72 p.
附註:	Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
Contained By:	Dissertations Abstracts International85-03B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30639493
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. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 72 p.

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

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

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.

ISBN: 9798380332811Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Braid skein algebra

A Floer-Theoretic Interpretation of the Polynomial Representation of the Double Affine Hecke Algebra.
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100 1 $a Reisin-Tzur, Eilon. $3 3769908
245 1 2 $a A Floer-Theoretic Interpretation of the Polynomial Representation of the Double Affine Hecke Algebra.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 72 p.
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.
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.
590 $a School code: 0031.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Braid skein algebra
653 $a Hecke algebra
653 $a Geometry
653 $a Heegaard Floer homology
653 $a Topology
690 $a 0405
690 $a 0642
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 2096468
773 0 $t Dissertations Abstracts International $g 85-03B.
790 $a 0031
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30639493