南開科技大學圖書館 |

言語: 日文

ヘルプ

南開科技大學

圖書館首頁

編目中圖書申請

ログイン

前に戻る

スイッチ: ラベル | MARC形式 | 国際標準書誌記述(ISBD)

Vanishing and non-vanishing criteria...

Purbhoo, Kevin.

Vanishing and non-vanishing criteria for branching Schubert calculus.

レコード種別:	コンピュータ・メディア : 単行資料
タイトル / 著者:	Vanishing and non-vanishing criteria for branching Schubert calculus./
著者:	Purbhoo, Kevin.
記述:	96 p.
注記:	Source: Dissertation Abstracts International, Volume: 65-09, Section: B, page: 4611.
含まれています:	Dissertation Abstracts International65-09B.
主題:	Mathematics. -
電子資源:	Download fulltext (下載全文)
国際標準図書番号 (ISBN):	049605371X

Vanishing and non-vanishing criteria for branching Schubert calculus.
Purbhoo, Kevin.

Vanishing and non-vanishing criteria for branching Schubert calculus. - 96 p.

Source: Dissertation Abstracts International, Volume: 65-09, Section: B, page: 4611.

Thesis (Ph.D.)--University of California, Berkeley, 2004.

We investigate several related vanishing problems in Schubert calculus. First we consider the multiplication problem. For any complex reductive Lie group G, many of the structure constants of the ordinary cohomology ring H*(G/B; Z ) vanish in the Schubert basis, and the rest are strictly positive. More generally, one can look at vanishing of Schubert intersection numbers, which generalise the multiplication problem to looking at products of more than two classes. We present a combinatorial game, the "root game", which provides some criteria for determining which of the Schubert intersection numbers vanish. The definition of the root game is manifestly invariant under automorphisms of G, and under permutations of the classes intersected. Although the criteria given by the root game are not proven to cover all cases, in practice they work very well, giving a complete answer to the question for G = GL(n, C ), n ≤ 7.

ISBN: 049605371XSubjects--Topical Terms:

146772
Mathematics.

Vanishing and non-vanishing criteria for branching Schubert calculus.
LDR:03722nmm 2200289 4500 001 1000004316
005 20051102155245.5
008 141201s2004 eng d
020 $a 049605371X
035 $a (UnM)AAI3146983
035 $a AAI3146983
040 $a UnM $c UnM{me_controlnum}
100 1 $a Purbhoo, Kevin. $3 1000005647
245 1 0 $a Vanishing and non-vanishing criteria for branching Schubert calculus.
300 $a 96 p.
500 $a Source: Dissertation Abstracts International, Volume: 65-09, Section: B, page: 4611.
500 $a Chair: Allen Knutson.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 2004.
520 $a We investigate several related vanishing problems in Schubert calculus. First we consider the multiplication problem. For any complex reductive Lie group G, many of the structure constants of the ordinary cohomology ring H*(G/B; Z ) vanish in the Schubert basis, and the rest are strictly positive. More generally, one can look at vanishing of Schubert intersection numbers, which generalise the multiplication problem to looking at products of more than two classes. We present a combinatorial game, the "root game", which provides some criteria for determining which of the Schubert intersection numbers vanish. The definition of the root game is manifestly invariant under automorphisms of G, and under permutations of the classes intersected. Although the criteria given by the root game are not proven to cover all cases, in practice they work very well, giving a complete answer to the question for G = GL(n, C ), n ≤ 7.
520 $a The root game can be used to study the vanishing problem for multiplication on H*(G/P) (where P ⊂ G is a parabolic subgroup) by pulling back the (G/P)-Schubert classes to H* (G/B). In the case where G/P is a Grassmannian, the Schubert structure constants are Littlewood-Richardson numbers. We show that the root game gives a necessary and sufficient rule for non-vanishing of Schubert calculus on Grassmannians. A Littlewood-Richardson number is non-zero if and only if it is possible to win the corresponding root game. More generally, the rule can be used to determine whether or not a product of several Schubert classes on Grl(n, C ) is non-zero in a manifestly symmetric way. We give a geometric interpretation of root games for Grassmannian Schubert problems.
520 $a Finally, and most generally we look at the vanishing problem for branching Schubert calculus. If K' &rarrhk; K is an inclusion of compact connected Lie groups, there is an induced map H*(K/T) → H*(K'/T ') on the cohomology of the homogeneous spaces. The image of a Schubert class under this map is a positive sum of Schubert classes on K'/T'. We investigate the problem of determining which Schubert classes appear with non-zero coefficient. This problem plays an important role in representation theory and symplectic geometry, as shown in [Berenstein-Sjamaar 2000]. The vanishing problems for multiplication of Schubert calculus can be seen as special cases of the branching problem. We develop root games for branching Schubert calculus, which give a vanishing criterion, and a non-vanishing criterion, for this problem. Again, these two criteria are not enough to give a complete answer to the problem; however they are applicable to a large number of cases. We include a number of examples of root games to illustrate both their simplicity and applicability.
590 $a School code: 0028.
650 4 $a Mathematics. $3 146772
690 $a 0405
710 2 0 $a University of California, Berkeley. $3 1000005479
773 0 $t Dissertation Abstracts International $g 65-09B.
790 1 0 $a Knutson, Allen, $e advisor
790 $a 0028
791 $a Ph.D.
792 $a 2004
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3146983 $z Download fulltext (下載全文)

館藏地: 出版年: 卷號:

館藏

此限制條件找不到符合的館藏，請您更換限制條件。

建立或儲存個人書籤

書目轉出

取書館別