关于与约当分拆相关的周期性与对偶性的进一步研究
表示论
2019-07-16 v1
摘要
设 J r J_r J r p p p F F F 1 1 1 r × r r \times r r × r r ≤ s r \leq s r ≤ s r r r s s s r s × r s r s \times r s r s × r s J r ⊗ J s J_{r} \otimes J_{s} J r ⊗ J s J λ 1 ⊕ J λ 2 ⊕ ⋯ ⊕ J λ r J_{\lambda_1} \oplus J_{\lambda_2} \oplus \dots \oplus J_{\lambda_{r}} J λ 1 ⊕ J λ 2 ⊕ ⋯ ⊕ J λ r λ 1 ≥ λ 2 ≥ ⋯ ≥ λ r > 0 \lambda_1 \geq \lambda_2 \geq \dots \geq \lambda_{r}>0 λ 1 ≥ λ 2 ≥ ⋯ ≥ λ r > 0 r s r s r s λ ( r , s , p ) = ( λ 1 , λ 2 , … , λ r ) \lambda(r,s,p)=(\lambda_1,\lambda_2,\dots, \lambda_{r}) λ ( r , s , p ) = ( λ 1 , λ 2 , … , λ r ) r r r s s s p p p ( λ 1 , λ 2 , … , λ r ) = ( μ 1 , … , μ 1 ⏞ m 1 , μ 2 , … , μ 2 ⏞ m 2 , … , μ k , … , μ k ⏞ m k ) = ( m 1 ⋅ μ 1 , … , m k ⋅ μ k ) , (\lambda_1,\lambda_2,\dots, \lambda_{r})=(\overbrace{\mu_1,\dots,\mu_1}^{m_1},\overbrace{\mu_2,\dots,\mu_2}^{m_2},\dots, \overbrace{\mu_k,\dots,\mu_k}^{m_k}) =(m_1 \cdot \mu_1, \dots,m_k \cdot \mu_k), ( λ 1 , λ 2 , … , λ r ) = ( μ 1 , … , μ 1 m 1 , μ 2 , … , μ 2 m 2 , … , μ k , … , μ k m k ) = ( m 1 ⋅ μ 1 , … , m k ⋅ μ k ) , μ 1 > μ 2 > ⋯ > μ k > 0 \mu_1>\mu_2>\dots>\mu_k>0 μ 1 > μ 2 > ⋯ > μ k > 0 r r r ( m 1 , … , m k ) (m_1,\dots,m_k) ( m 1 , … , m k ) c ( r , s , p ) c(r,s,p) c ( r , s , p ) r ≤ p β r \leq p^\beta r ≤ p β c ( r , s , p ) c(r,s,p) c ( r , s , p ) s s s p β p^\beta p β
引用
@article{arxiv.1907.06519,
title = {More on Periodicity and Duality associated with Jordan partitions},
author = {Michael J. J. Barry},
journal= {arXiv preprint arXiv:1907.06519},
year = {2019}
}
备注
6 pages