| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 黃曦嶢 | zh_TW |
| DC.creator | Si-Yao Huang | en_US |
| dc.date.accessioned | 2021-12-13T07:39:07Z | |
| dc.date.available | 2021-12-13T07:39:07Z | |
| dc.date.issued | 2021 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=108221003 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.abstract | 在我和老師的會議中，認為型態(C1∨, C1)的通用加法DAHA中能看到Leonard三元組，所以我們利用學術網站上的相關論文，並且透過通用 Racah代數來得到以下結果。
假設 ? 是一個特徵為零的代數封閉體。通用Racah代數R是由A,B,C,D生成的單位結合?-代數，關係式為 [A, B] = [B, C] = [C, A] = 2D 並且每個
[A, D] + AC − BA, [B, D] + BA − CB, [C, D] + CB – AC
在R上皆可換。
型態 (C1∨, C1) 的通用加法 DAHA (雙仿射 Hecke 代數)H是由 t_0,t_1,t_2,t_3 生成的單位結合 ?-代數，關係式為
t_0+t_1+t_2+t_3= -1，
t_0^2,
t_1^2,
t_2^2,
t_3^2 皆可換。
任何H-module 都可以被認為是一個R-module 透過 ?-代數同態將 送到H，由下式給出
A 送到 (t_0+t_1-1)(t_0+t_1+1)/4，
B 送到 (t_0+t_2-1)(t_0+t_2+1)/4，
C 送到 (t_0+t_3-1)(t_0+t_3+1)/4。
令 V 表示有限維不可分 H-module。 在本文中，我們展示了 A, B, C
在 V 上可對角化若且為若 A, B, C 在 R-module V 的所有合成因子上為Leonard 三元組。 | zh_TW |
| dc.description.abstract | In the meeting, I thought that the Leonard triples can be seen in the universal additive DAHA of type (C1∨, C1), so we used the relevant papers on the academic website and obtained the following results through the universal Racah algebra.
Suppose that ? is an algebraically closed field with characteristic 0. The universal Racah algebra R is a unital associative ?-algebra generated by A, B, C, D and the relations state that [A, B] = [B, C] = [C, A] = 2D and each of
[A, D] + AC - BA, [B, D] + BA - CB, [C, D] + CB - AC
is central in R. The universal additive DAHA (double affine Hecke algebra) H of type (C1∨, C1) is a unital associative ?-algebra generated by t_i (i=0,1,2,3) and the relations state that
t_0+t_1+t_2+t_3= -1，
t_i^2 is central for all i = 0, 1, 2, 3.
Any H-module can be considered as a R-module via the ?-algebra homomorphism R to H given by
A mapsto (t_0+t_1-1)(t_0+t_1+1)/4,
B mapsto (t_0+t_2-1)(t_0+t_2+1)/4,
C mapsto (t_0+t_3-1)(t_0+t_3+1)/4.
Let V be a finite-dimensional irreducible H-module. In this paper we show that A, B, C are diagonalizable on V if and only if A, B, C act as Leonard triples
on each composition factor of the R-module V. | en_US |
| DC.subject | 三元組 | zh_TW |
| DC.subject | Leonard | en_US |
| DC.subject | DAHA | en_US |
| DC.title | The Leonard triples and the universal additive DAHA of type (C1ˇ,C1) | en_US |
| dc.language.iso | en_US | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |