RUS  ENG
Full version
JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications

SIGMA, 2021, Volume 17, 038, 9 pp. (Mi sigma1721)

The Primitive Derivation and Discrete Integrals
Daisuke Suyama, Masahiko Yoshinaga

References

1. Abe T., Enomoto N., Feigin M., Yoshinaga M., Free reflection multiarrangements and quasi-invariants, in preparation
2. Abe T., Suyama D., “A basis construction of the extended Catalan and Shi arrangements of the type $A_2$”, J. Algebra, 493 (2018), 20–35, arXiv: 1312.5524  crossref  mathscinet  zmath  scopus
3. Athanasiadis C. A., “On free deformations of the braid arrangement”, European J. Combin., 19 (1998), 7–18  crossref  mathscinet  zmath  scopus
4. Bandlow J., Musiker G., “A new characterization for the $m$-quasiinvariants of $S_n$ and explicit basis for two row hook shapes”, J. Combin. Theory Ser. A, 115 (2008), 1333–1357, arXiv: 0707.3174  crossref  mathscinet  zmath  elib  scopus
5. Chalykh O. A., Veselov A. P., “Commutative rings of partial differential operators and Lie algebras”, Comm. Math. Phys., 126 (1990), 597–611  crossref  mathscinet  zmath  adsnasa  scopus
6. Edelman P. H., Reiner V., “Free arrangements and rhombic tilings”, Discrete Comput. Geom., 15 (1996), 307–340  crossref  mathscinet  zmath  scopus
7. Feigin M., Private communication
8. Feigin M., Veselov A. P., “Quasi-invariants of Coxeter groups and $m$-harmonic polynomials”, Int. Math. Res. Not., 2002 (2002), 521–545, arXiv: math-ph/0105014  crossref  mathscinet  zmath  scopus
9. Felder G., Veselov A. P., “Action of Coxeter groups on $m$-harmonic polynomials and Knizhnik–Zamolodchikov equations”, Mosc. Math. J., 3 (2003), 1269–1291, arXiv: math.QA/0108012  mathnet  crossref  mathscinet  zmath
10. Gao R., Pei D., Terao H., “The Shi arrangement of the type $D_\ell$”, Proc. Japan Acad. Ser. A Math. Sci., 88 (2012), 41–45, arXiv: 1109.1381  crossref  mathscinet  zmath  scopus
11. Orlik P., Terao H., Arrangements of hyperplanes, Grundlehren der Mathematischen Wissenschaften, 300, Springer-Verlag, Berlin, 1992  crossref  mathscinet  zmath
12. Postnikov A., Stanley R. P., “Deformations of Coxeter hyperplane arrangements”, J. Combin. Theory Ser. A, 91 (2000), 544–597, arXiv: math.CO/9712213  crossref  mathscinet  zmath  scopus
13. Saito K., “Theory of logarithmic differential forms and logarithmic vector fields”, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 27 (1980), 265–291  mathscinet  zmath
14. Saito K., “Period mapping associated to a primitive form”, Publ. Res. Inst. Math. Sci., 19 (1983), 1231–1264  crossref  mathscinet  zmath  scopus
15. Saito K., “On a linear structure of the quotient variety by a finite reflexion group”, Publ. Res. Inst. Math. Sci., 29 (1993), 535–579  crossref  mathscinet  zmath
16. Saito K., “Uniformization of the orbifold of a finite reflection group”, Frobenius Manifolds, Aspects Math., E36, Friedr. Vieweg, Wiesbaden, 2004, 265–320  crossref  mathscinet
17. Shi J.-Y., The Kazhdan–Lusztig cells in certain affine Weyl groups, Lecture Notes in Mathematics, 1179, Springer-Verlag, Berlin, 1986  crossref  mathscinet  zmath
18. Suyama D., “A basis construction for the Shi arrangement of the type $B_\ell$ or $C_\ell$”, Comm. Algebra, 43 (2015), 1435–1448, arXiv: 1205.6294  crossref  mathscinet  zmath  scopus
19. Suyama D., Terao H., “The Shi arrangements and the Bernoulli polynomials”, Bull. Lond. Math. Soc., 44 (2012), 563–570, arXiv: 1103.3214  crossref  mathscinet  zmath  scopus
20. Terao H., “Multiderivations of Coxeter arrangements”, Invent. Math., 148 (2002), 659–674, arXiv: math.CO/0011247  crossref  mathscinet  zmath  adsnasa  scopus
21. Terao H., “The Hodge filtration and the contact-order filtration of derivations of Coxeter arrangements”, Manuscripta Math., 118 (2005), 1–9, arXiv: math.CO/0205058  crossref  mathscinet  zmath  scopus
22. Tsuchida T., “On quasiinvariants of $S_n$ of hook shape”, Osaka J. Math., 47 (2010), 461–485, arXiv: 0807.1892  mathscinet  zmath  elib
23. Yoshinaga M., “The primitive derivation and freeness of multi-Coxeter arrangements”, Proc. Japan Acad. Ser. A Math. Sci., 78 (2002), 116–119, arXiv: math.CO/0206216  crossref  mathscinet  zmath  scopus
24. Yoshinaga M., “Characterization of a free arrangement and conjecture of Edelman and Reiner”, Invent. Math., 157 (2004), 449–454  crossref  mathscinet  zmath  adsnasa  scopus
25. Yoshinaga M., “Freeness of hyperplane arrangements and related topics”, Ann. Fac. Sci. Toulouse Math., 23 (2014), 483–512, arXiv: 1212.3523  crossref  mathscinet  zmath
26. Ziegler G. M., “Multiarrangements of hyperplanes and their freeness”, Singularities (Iowa City, IA, 1986), Contemp. Math., 90, Amer. Math. Soc., Providence, RI, 1989, 345–359  crossref  mathscinet


© Steklov Math. Inst. of RAS, 2025