- p01. 1. Introduction
- p04. 2. Preliminaries
- p06. 3. Exclusion of multiple flag varieties of infinite type
- p06. 3.1. Proof of Proposition 1.2.
- p08. 3.2. Proof of Proposition 1.3.
- p10. 3.3. Proof of Proposition 1.4.
- p11. 3.4. Proof of Proposition 1.5.
- p14. 3.5. Case of a=(n), b=$(\beta)$ with $4\le \beta \le n-2$.
- p19. 3.6. Proof of Proposition 1.6(ii).
- p20. 3.7. Proof of Proposition 1.6(iii).
- p21. 4. Triple flag varieties of finite type.
- p22. 5. Review of technical results in [M15].
- 5.1
- 5.2
- 5.3
- 5.4
- p28. 6 Proof of Proposition 4.1.
- p28. 6.1. Reduction of flags in $U_+$.
- p31. 6.2. Proof of (i) and (ii).
- p32. 6.3. Proof of (iii) and (iv).
- p36. 6.4. Proof of (v).
- p37. 7. Proof of Proposition 4.2 and 4.3.
- p37. 7.1. Proof of Proposition 4.2.
(A), (B), (C), (D), (D.1), (D.1.1), (D.1.2), (D.1.3), (D.1.4), (D.1.5), (D.1.6), (D.2), (D.3), (D.3.1), (D.3.2), (D.3.3), (D.3.4), (D.3.5), (D.3.6), (D.4), (D.5), (D.5.1), (D.5.2), (D.5.3), (D.6), (D.6.1), (D.6.2), (D.6.2.1), (D.6.2.2), (D.6.2.3), (D.6.2.4), (D.6.2.5), (D.6.3).
- p45. 7.2. Proof of Proposition 4.3.
- p47. 8. Proof of Proposition 4.4.
- p47. 8.1. Proof of the case $b=(\beta)=(n-1)$.
(A), (B),(C).
- p49. 8.2. Proof of the case of $b=(1,n-1)$.
(A),(B),(C),(D),(E),(F).
- p54. 9. Proof of Proposition 4.5.
(A),(B),(C),(D),(E),(F), (G).
- p61. 10. Proof of Proposition 4.6.
(A)-(I).
- p69. 11. Proof of Proposition 4.7.
(A)-(E).
- p76. 12. Appendix
- p76. 12.1. Two lemmas.
- p77. 12.2. Extensions of Proposition 6.3 in [M15].
- p82. 12.3. Orbit decompositions of the full flag variety.
(A)-(K).
- p91. 12.4. A lemma.
- p92. 12.5. Lemmas related with $SL_2(F)$.
- p96. References
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