榎本 直也
| 共通教育部（研究科） | 准教授 |
| 共通教育部（学域） | 准教授 |
| 情報学専攻 | 准教授 |
| Ⅱ類（融合系） | 准教授 |
研究者情報
経歴
研究活動情報
論文
- New series in the Johnson cokernels of the mapping class groups of surfaces
Naoya Enomoto; Takao Satoh
ALGEBRAIC AND GEOMETRIC TOPOLOGY, GEOMETRY & TOPOLOGY PUBLICATIONS, 14巻, 2号, 掲載ページ 627-669, 出版日 2014年, 査読付, Let Sigma(g, 1) be a compact oriented surface of genus g with one boundary component, and M-g,M- 1 its mapping class group. Morita showed that the image of the kth Johnson homomorphism tau(M)(k) M-g,M- 1 is contained in the kernel h(g, 1) (k) of an Sp-equivariant surjective homomorphism H circle times(Z) L-2 g (k+1) -> L-2g (k+2), where H := H-1 (Sigma(g, 1), Z) and L-2g (k) is the degree k part of the free Lie algebra L-2g generated by H. In this paper, we study the Sp-module structure of the cokernel h(g,1)(Q) (k) /Im (tau(M)(k,Q)) of the rational Johnson homomorphism tau(M)(k,Q) := tau(M)(k) circle times id(Q), where h(g,1)(Q) (k):= h(g,1) (k) circle times(Z)Q . In particular, we show that the irreducible Sp- module corresponding to a partition [1(k)] appears in the kth Johnson cokernel for any k 1 (mod 4) and k >= 5 with multiplicity one. We also give a new proof of the fact due to Morita that the irreducible Sp- module corresponding to a partition O k _ appears in the Johnson cokernel with multiplicity one for odd k >= 3.
The strategy of the paper is to give explicit descriptions of maximal vectors with highest weight [1(k)] and [k] in the Johnson cokernel. Our construction is inspired by the Brauer-Schur-Weyl duality between Sp(2g, Q) and the Brauer algebras, and our previous work for the Johnson cokernel of the automorphism group of a free group.
研究論文（学術雑誌）, 英語 - Sp-Irreducible Components in the Johnson Cokernels of the Mapping Class Groups of Surfaces, I
Hikoe Enomoto; Naoya Enomoto
JOURNAL OF LIE THEORY, HELDERMANN VERLAG, 24巻, 3号, 掲載ページ 687-704, 出版日 2014年, 査読付, In "N. Enomoto and T. Satoh, New series in the Johnson cokernels of the mapping class groups of surfaces, to appear in Algebraic and Geometric Topology," the second author and Takao Satoh introduced a new class in the Johnson cokernels for the mapping class groups of surfaces, and detected a series of Sp-irreducible components [1(4m+1)] (m >= 1) in this class. In this paper, we detect another series [lambda] in this class for some hook type partitions lambda.
研究論文（学術雑誌）, 英語 - On the derivation algebra of the free Lie algebra and trace maps
Naoya Enomoto; Takao Satoh
ALGEBRAIC AND GEOMETRIC TOPOLOGY, GEOMETRY & TOPOLOGY PUBLICATIONS, 11巻, 5号, 掲載ページ 2861-2901, 出版日 2011年, 査読付, We mainly study the derivation algebra of the free Lie algebra and the Chen Lie algebra generated by the abelianization H of a free group, and trace maps. To begin with, we give the irreducible decomposition of the derivation algebra as a GL(n, Q)-module via the Schur-Weyl duality and some tensor product theorems for GL(n, Q). Using them, we calculate the irreducible decomposition of the images of the Johnson homomorphisms of the automorphism group of a free group and a free metabelian group.
Next, we consider some applications of trace maps: Morita's trace map and the trace map for the exterior product of H. First, we determine the abelianization of the derivation algebra of the Chen Lie algebra as a Lie algebra, and show that the abelianization is given by the degree one part and Morita's trace maps. Second, we consider twisted cohomology groups of the automorphism group of a free nilpotent group. In particular, we show that the trace map for the exterior product of H defines a nontrivial twisted second cohomology class of it.
研究論文（学術雑誌）, 英語 - A Quiver Construction of Symmetric Crystals
Naoya Enomoto
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, OXFORD UNIV PRESS, 12巻, 12号, 掲載ページ 2200-2247, 出版日 2009年, 査読付, In the papers [4-6] with Masaki Kashiwara, the author introduced the notion of symmetric crystals and presented the Lascoux-Leclerc-Thibon-Ariki-type conjectures for the affine Hecke algebras of type B. Namely, we conjectured that certain composition multiplicities and branching rules for the affine Hecke algebras of type B are described by using the lower global basis of symmetric crystals of V-theta(lambda). In the present paper, we prove the existence of crystal bases and global bases of V-theta(O) for any symmetric quantized Kac-Moody algebra by using a geometry of quivers (with a Dynkin diagram involution). This is analogous to George Lusztig's geometric construction of U-nu(-) and its lower global basis.
研究論文（学術雑誌）, 英語 - Composition factors of polynomial representation of DAHA and q-decomposition numbers
Naoya Enomoto
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, KINOKUNIYA CO LTD, 49巻, 3号, 掲載ページ 441-473, 出版日 2009年, 査読付, We determine the composition factors of the polynomial representation of DAHA, conjectured by M. Kasatani in [Kasa, Conjecture 6.4.]. He constructed an increasing sequence of subrepresentations in the polynomial representation of DAHA using the "multi-wheel condition", and conjectured that it is a composition series. On the other hand, DAHA has two degenerate versions called the "degenerate DAHA" and the "rational DAHA". The category O of modules over these three algebras and the category of modules over the nu-Schur algebra are closely related. By using this relationship, we reduce the determination of composition factors of polynomial representations of DAHA to the determination of the composition factors of the Weyl module W(nu)((n)) for the nu-Schur algebra. By using the LLT-Ariki type theorem of nu-Schur algebra proved by Varagnolo-Vasserot, we determine the composition factors of W(nu)((n)) by (calculating the upper global basis and crystal basis of Fock space of U(q)((sl) over cape) when nu is a primitive l-th root of unity.
This result gives a different way from the determination of decomposition number of W(nu)((n)) by H. Miyachi or B. Ackermann via the modular representation theory of the general linear groups.
研究論文（学術雑誌）, 英語 - Symmetric crystals for $gl_\infty$
榎本直也; 柏原正樹
Publ. Res. Inst. Math. Sci., 44巻, 3号, 掲載ページ 837-891, 出版日 2008年, 査読付
研究論文（学術雑誌）, 英語 - Symmetric crystals and affine Hecke algebras of type B
Naoya Enomoto; Masaki Kashiwara
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, 82巻, 8号, 掲載ページ 131-136, 出版日 2006年10月, 査読付, The Lascoux-Leclerc-Thibon conjecture, reformulated and solved by S. Ariki, asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent sub roup of the group associated with a Lie algebra g where g is gl(infinity) or the affine Lie algebra A(l)((1)), and the irreducible representations correspond to the upper global bases. In this note, we formulate analogous conjectures for certain classes of irreducible representations of affine Hecke algebras of type B.
研究論文（学術雑誌）, 英語 - Classification of the irreducible representations of the affine Hecke algebra of type B-2 with unequal parameters
Naoya Enomoto
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, KINOKUNIYA CO LTD, 46巻, 2号, 掲載ページ 259-273, 出版日 2006年, 査読付
研究論文（学術雑誌）, 英語
担当経験のある科目_授業
- Fundamentals of Algebra
The University of Electro-Communications - 代数学基礎論
電気通信大学 - Introduction to Modern Mathematics B
The University of Electro-Communications - 現代数学入門B
電気通信大学 - Linear Algebra I
The University of Electro-Communications - Advanced Topics in Algebra
The University of Electro-Communications - 代数学特論
電気通信大学 - Exercise in Mathematics Ⅱ
The University of Electro-Communications - 数学演習第二
電気通信大学 - Linear Algebra II
The University of Electro-Communications - 線形代数学第二
電気通信大学 - Linear Algebra I(A)
Nara Women’s University - 線形代数学Ⅰ（A)
奈良女子大学 - Exercise in Mathematics Ⅰ
The University of Electro-Communications - 数学演習第一
電気通信大学 - Linear Algebra Ⅰ
The University of Electro-Communications - 線形代数学第一
電気通信大学 - 数学特別講義I
奈良女子大学 - 数学特別講義I
奈良女子大学 - 解析概論II
奈良女子大学 - 解析概論II
奈良女子大学 - 線型代数学演習A,B
京都大学 - 線型代数学演習A,B
京都大学 - 集合・位相演習
奈良女子大学 - 集合・位相演習
奈良女子大学 - 線形代数学B[再履修]
京都大学 - 線形代数学B[再履修]
京都大学 - 線型代数学演習B
京都大学 - 線型代数学演習B
京都大学