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Hypergeometric Sheaves, Weil Represe...

Lee, Tae Young,

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Hypergeometric Sheaves, Weil Representations, and Finite General Linear Groups /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Hypergeometric Sheaves, Weil Representations, and Finite General Linear Groups // Tae Young Lee.
作者:	Lee, Tae Young,
面頁冊數:	1 electronic resource (126 pages)
附註:	Source: Dissertations Abstracts International, Volume: 85-11, Section: B.
Contained By:	Dissertations Abstracts International85-11B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31142839
ISBN:	9798382760490

Hypergeometric Sheaves, Weil Representations, and Finite General Linear Groups /
Lee, Tae Young,

Hypergeometric Sheaves, Weil Representations, and Finite General Linear Groups /Tae Young Lee. - 1 electronic resource (126 pages)

Source: Dissertations Abstracts International, Volume: 85-11, Section: B.

Abhyankar's conjecture, proved by Raynaud, Harbater and Pop, characterizes the finite quotient groups of the etale fundamental group of affine algebraic groups over algebraically closed fields of positive characteristic. Katz, Rojas-Leon and Tiep, in their recent series of papers, realized many of these groups as monodromy groups of certain "easy to remember" local systems over the affine line \uD835\uDD381 and the multiplicative group \uD835\uDD3Em. On \uD835\uDD3Em, they used the hypergeometric sheaves to realize these groups. Furthermore, they classified the finite groups that can be possibly realized by irreducible hypergeometric sheaves.In this dissertation, we give the complete solution of this problem for the hypergeometric sheaves and almost quasisimple groups with the unique nonabelian composition factor PSLn(q) with n ≥ 3. Specifically, we fully generalize a construction of Katz and Tiep, and prove that there is no other irreducible hypergeometric sheaf with such geometric monodromy group. This includes several results about the irreducible Weil representations of GLn(q). We also present analogous results on the Weil representations of GUn(q), which is likely to be needed in the classification of the hypergeometric sheaves in the case of PSUn(q).

English

ISBN: 9798382760490Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Finite general linear groups

Hypergeometric Sheaves, Weil Representations, and Finite General Linear Groups /
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245 1 0 $a Hypergeometric Sheaves, Weil Representations, and Finite General Linear Groups / $c Tae Young Lee.
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336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertations Abstracts International, Volume: 85-11, Section: B.
500 $a Advisors: Tiep, Pham Huu Committee members: Retakh, Vladimir; Matveev, Konstantin; Katz, Nicholas.
502 $b Ph.D. $c Rutgers The State University of New Jersey, School of Graduate Studies $d 2024.
520 $a Abhyankar's conjecture, proved by Raynaud, Harbater and Pop, characterizes the finite quotient groups of the etale fundamental group of affine algebraic groups over algebraically closed fields of positive characteristic. Katz, Rojas-Leon and Tiep, in their recent series of papers, realized many of these groups as monodromy groups of certain "easy to remember" local systems over the affine line \uD835\uDD381 and the multiplicative group \uD835\uDD3Em. On \uD835\uDD3Em, they used the hypergeometric sheaves to realize these groups. Furthermore, they classified the finite groups that can be possibly realized by irreducible hypergeometric sheaves.In this dissertation, we give the complete solution of this problem for the hypergeometric sheaves and almost quasisimple groups with the unique nonabelian composition factor PSLn(q) with n ≥ 3. Specifically, we fully generalize a construction of Katz and Tiep, and prove that there is no other irreducible hypergeometric sheaf with such geometric monodromy group. This includes several results about the irreducible Weil representations of GLn(q). We also present analogous results on the Weil representations of GUn(q), which is likely to be needed in the classification of the hypergeometric sheaves in the case of PSUn(q).
546 $a English
590 $a School code: 0190
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Finite general linear groups
653 $a Finite general unitary groups
653 $a Hypergeometric sheaves
653 $a Monodromy groups
653 $a Weil representations
690 $a 0405
690 $a 0642
690 $a 0364
710 2 $a Rutgers The State University of New Jersey, School of Graduate Studies. $b Mathematics. $e degree granting institution. $3 3823021
720 1 $a Tiep, Pham Huu $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 85-11B.
790 $a 0190
791 $a Ph.D.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31142839