0-Hecke modules associated with regular Schur labeled skew shape posets and their connections to generic Hecke modules
- 주제(키워드) Hecke algebra , Grothendieck ring , symmetric function , quasisymmetric function , Schur labeled skew shape posets , specialization
- 발행기관 서강대학교 일반대학원
- 지도교수 오영탁
- 발행년도 2026
- 학위수여년월 2026. 2
- 학위명 박사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000082715
- UCI I804:11029-000000082715
- 본문언어 영어
- 저작권 논문은 저작권에 의해 보호받습니다.
목차
1 Introduction 1
1.1 0-Hecke modules associated with regular Schur labeled skew shape posets 3
1.2 Specializations and the functors induced by them 4
1.3 Main results 5
1.4 Organization 7
2 Preliminaries 9
2.1 Compositions, Young diagrams, and bijective tableaux 9
2.2 Symmetric group, Bruhat order, and weak Bruhat order 11
2.3 Symmetric functions and quasisymmetric functions 13
2.4 Hecke algebras and their representation theory 14
2.4.1 The generic Hecke algebra and the Frobenius characteristic 17
2.4.2 The 0-Hecke algebra and the quasisymmetric characteristic 18
3 Schur labeled skew shape posets and regular posets 21
3.1 Schur labeled skew shape posets 21
3.2 Regular posets 23
4 Regular Schur labeled skew shape posets and their 0-Hecke modules 28
4.1 The weak Bruhat interval structure of ΣL(P ) for P RSPn 29
4.2 An equivalence relation on Int(n) 35
4.3 The classification of MP 's for P RSPn 47
4.4 A characterization of regular Schur labeled skew shape posets P and distinguished filtrations of MP 57
4.4.1 A characterization of regular Schur labeled skew shape posets 57
4.4.2 Distinguished filtrations of MP for P RSPn 62
4.5 A tableau description of MP for P RSPn 67
5 Connections between 0-Hecke modules and Hecke modules 70
5.1 Functors induced by specializations 71
5.1.1 The tensor functor S θ 71
5.1.2 Specialization functors 73
5.2 Character theory of Hecke algebras 77
5.2.1 Character theory of generic Hecke algebras 78
5.2.2 Character theory of 0-Hecke algebras 80
5.2.3 A characterization of 0-Hecke modules having symmetric characteristic image 81
5.3 0-Hecke modules obtained from specializations 86
5.3.1 0-Hecke modules obtained from skew Specht modules 86
5.3.2 0-Hecke modules obtained from KazhdanLusztig cell modules 93
5.4 Properties of 0-Hecke modules via specialization 101
5.4.1 A relationship between characteristics via specializations 102
5.4.2 Restriction of skew Specht modules and comparison via the specialization functor 103
5.4.3 Hom-sets between 0-Hecke modules obtained from Kazhdan-Luszitg cell modules 104
