PUBLICATIONS


  1. Cohomology of tensor product of quantum planes

    Rendiconti Lincei - Matematica e applicazioni Serie IX, III, 5-13 , 1992.

  2. A characterization of a special ordering in a root system

    Proceedings of the A.M.S., 120, 661-665, 1994.

  3. Convex orderings and symmetric group

    Communications in Algebra, 22, 4089-4095, 1994.

  4. Ordinamenti compatibili nei sistemi di radici

    Tesi di Dottorato (PhD Thesis), Universita' di Pisa, 1994.

    (Abstract) (Riassunto)

  5. Convex orderings in affine root systems

    Journal of Algebra, 172, 613-623, 1995.

  6. Convex orderings in affine root systems II

    Journal of Algebra, 186,72-91, 1996.

  7. Representations of the Brauer algebra and Littlewood's restriction rules

    (with F. Gavarini), Journal of Algebra, 194, n. 1 , 275-298, 1997.

  8. Affine permutations and inversion multigraphs

    Electronic Journal of Combinatorics, Vol. 4, 1997, n.5

  9. Invarianti di nodi

    (with C. Procesi, survey monograph; QUADERNI DELL'U.M.I n.45).

  10. The structure of total reflection orders in affine root systems

    (with P. Cellini), Journal of Algebra, 205 (n.1), 207-226, 1998.

  11. A combinatorial approach to the fusion process for the symmetric group

    (with V. Guizzi), European Journal of Combinatorics, 19, 835-845, 1998

  12. A root system approach to minimal coset representatives

    Proceedings of FPSAC '99, 429--437, 1999.

  13. A root system criterion for fully commutative and short braid-avoiding elements in affine Weyl groups

    (with P.Cellini), 1997, Journal of Algebraic Combinatorics, 11, 5-16, 2000.

  14. ad-nilpotent ideals of a Borel subalgebra

    (with P. Cellini), Journal of Algebra, 225, 130--141, 2000

  15. Enumeration of ad-nilpotent ideals of a Borel subalgebra in type A by class of nilpotence

    (with L. Orsina), Comptes Rendus de l'Academie des Sciences,, t. 330, 651--655, 2000.

  16. Inversion tables and minimal left coset representatives for Weyl groups of classical type

    Journal of Pure and Applied Algebra, 161, 219-234, 2001.

  17. ad-nilpotent b-ideals in sl(n) having a fixed class of nilpotence: combinatorics and enumeration

    (with G. Andrews, C. Krattenthaler, L. Orsina) Transactions of the A.M.S., 354. 3835--3853, 2002

  18. Enumeration of ad-nilpotent b-ideals for simple Lie algebras

    (with C. Krattenthaler, L. Orsina), Adv. Appl. Math., 28, 478--522, 2002.

  19. ad-nilpotent ideals of a Borel subalgebra II

    (with P. Cellini) Journal of Algebra , 258, 1, 112--121 (2002)

  20. Compatible discrete series

    (with P. Cellini, P. Möseneder Frajria) Pacific Journal of mathematics , 212 (2), 201--230, (2003)

  21. Abelian ideals of Borel subalgebras and affine Weyl groups

    (with P. Cellini), Advances in mathematics , 187, 320--361, (2004), available on the ArXiv as ad-nilpotent ideals of a Borel subalgebra III

  22. Abelian subalgebras in Z_2-graded Lie algebras and affine Weyl groups

    (with P. Cellini, P. Möseneder Frajria), IMRN, n.43, 2281-2304, (2004)

  23. Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of Z_2-graded Lie algebras

    (with P. Cellini, V.G. Kac, P. Möseneder Frajria), Advances in mathematics , 207, (2006), 156--204

  24. The $\hat W$-orbit of $\rho$, Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of Z

    (with P. Cellini, P. Möseneder Frajria), Journal of Pure and Applied Algebra, 208 n.3 (2007), 1103--1119

  25. Casimir operators, abelian subspaces and u-cohomology

    (with P. Möseneder Frajria), Rendiconti di Matematica, 27, 265--276 (2007)

  26. Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting

    (with V.G. Kac, P. Möseneder Frajria), Advances in Mathematics , 217, 2485-2562, (2008)

  27. On the Kernel of the affine Dirac operator

    (with V.G. Kac, P. Möseneder Frajria), Moscow Mathematical Journal , Vol. 8, n.4, 759--788 (2008)

  28. Dirac operators in the affine setting

    Oberwolfach Reports, Vol. 6 n.1, 2009, 835--837

  29. ad-nilpotent ideals containing a fixed number of simple root spaces

    (with P. Cellini, P. Möseneder Frajria), Rendiconti di Matematica, vol. 29, serie 7; p. 153-162, (2009)

  30. Addendum to "On the Kernel of the affine Dirac operator"

    (with V.G. Kac, P. Möseneder Frajria), Moscow Mathematical Journal vol. 9; p. 927-929, (2009)

  31. Cyclic generators for irreducible representations of affine Hecke algebras

    (with V. Guizzi, M. Nazarov), Journal of Combinatorial Theory A vol. 117, p. 683--703 (2010)

  32. Denominator identities and Lie superalgebras (extended abstract)

    (with V. Kac, P. Möseneder Frajria), Proceedings of the FPSAC 2010, 839-850

  33. Irreducible representations of Yangians

    (with S. Khoroshkin, M. Nazarov), Journal of Algebra , 346 (2011) 189-226

  34. Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

    (with M. Gorelik, V. Kac, P. Möseneder Frajria) , Japanese Journal of Mathematics , 7 (2012),41--134

  35. On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces

    (with P. Cellini, P. Möseneder Frajria, M. Pasquali), Selecta Mathematica Volume 19, Issue 2 (2013), 399-437

  36. Advances in Lie Superalgebras

    (edited with M. Gorelik), Springer INdAM Series vol. 7

  37. Dirac operators and the Very Strange Formula for Lie superalgebras

    (with V. Kac, P. Möseneder Frajria), in "Advances in Lie Superalgebras", Springer INdAM Series vol. 7, 121--148

  38. Symmetries of abelian ideals of Borel subalgebras

    (with P. Cellini, P. Möseneder Frajria), Journal of Lie Theory, 24 (2014), No. 1, 199--224

  39. On special covariants in the exterior algebra of a simple Lie algebra

    (with C. Procesi, P. Möseneder Frajria C. De Concini), Rend. Lincei Mat. Appl. 25 (2014), 331-334

  40. The adjoint representation inside the exterior algebra of a simple Lie algebra

    (with C. Procesi, C. De Concini),  Advances in Mathematics , 280 (2015) 21-46

  41. The maximum cardinality of minimal inversion complete sets in finite reflection groups

    (with C. Malvenuto, P. Möseneder Frajria, L. Orsina), Journal of Algebra , 424 (2015), 330-356

  42. Conformal embeddings and simple current extensions

    (with V. Kac, P. Möseneder Frajria, F. Xu),   IMRN  (2015), no. 14, 5229–5288

  43. Finite vs infinite decompositions in conformal embeddings

    (with D. Adamovic, V. Kac, P. Möseneder Frajria, O. Perse),  Communications in Mathematical Physics, 348, 445-473 (2016)

  44. Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural results

    (with D. Adamovic, V. Kac, P. Möseneder Frajria, O. Perse),   Journal of Algebra, 500, (2018), 117-152

  45. Conformal embeddings of affine vertex algebras in minimal $W$-algebras II: decompositions

    (with D. Adamovic, V. Kac, P. Möseneder Frajria, O. Perse),  Japanese Journal of Mathematics, 12, (2017), n. 2, 261-315

  46. Spherical nilpotent orbits and abelian subalgebras in isotropy representations

    (with J. Gandini, P. Möseneder Frajria),    Journal of the London Mathematical Society, 95 (1), 323--352 (2017)

  47. On the classification of non-equal rank affine conformal embeddings and applications

    (with D. Adamovic, V. Kac, P. Möseneder Frajria, O. Perse),  Selecta Mathematica, 24, 2455-2498 (2018)

  48. On some modules of covariants for a reflection group

    (with C. De Concini),   Trans. Moscow Math. Soc.  (2017), 257--273

  49. An application of collapsing levels to the representation theory of affine vertex algebras

    (with D. Adamovic, V. Kac, P. Möseneder Frajria, O. Perse), IMRN, 2020, n. 13,  4104--4143

  50. Affine, Vertex and W-algebras

    (edited with D. Adamovic, Spinger Indam Series n. 37)

  51. Kostant's Lie pairs and conformal embeddings,

    52. (with D. Adamovic, V. Kac, P. Möseneder Frajria, "Affine, Vertex and W-algewbras", Spinger Indam Series n. 37, p. 1-22)

  52. The Bruhat order on abelian ideals of Borel subalgebra   

    53. (with A. Maffei, J. Gandini, P. Möseneder Frajria),  Transactions of the AMS, 373, n. 10  (2020), 6999-7018

  53. Conformal embeddings in affine vertex superalgebras          

    (with D. Adamovic, V. Kac, P. Möseneder Frajria, O. Perse, Advances in Mathematics, vol.360 (2020),  106918, 50 pp

  54. Nilpotent orbits of height 2 and involutions in the affine Weyl group

    55. (with J. Gandini,  P. Möseneder Frajria) Indagationes Mathematicae 31, (2020), n. 4, 568-594,

  55. Yangians vs minimal W-algebras: a surprizing coincidence

    56. (with V., Kac, P. Möseneder Frajria), Commun. Contemp. Math. 23 (2021), no. 4, 2050036,

  56. Invariant Invariant Hermitian forms on vertex algebras

    57. (with V. Kac, P. Möseneder Frajria), Commun. Contemp. Math.  24 (2022), no. 5, Paper No. 2150059, 41 pp. 

  57. On the semisimplicity of the category KL_k for affine Lie superalgebras

    58. (with D. Adamovic, P. Möseneder Frajria),  Advances in Mathematics,     405 (2022), Paper No. 108493, 35 pp.

  58. New approaches to studying conformal embeddings and conformal levels for W-algebras

    59. (with D. Adamovic and P. Moseneder Frajria), IMRN, 2023, no. 22, 19431–19475

  59. Unitarity of minimal W-algebras and their representations

    60. (with V. Kac and P. Moseneder Frajria),  Communications in Mathematical Physics, 401, 79--145, (2023)

  60. Defining relations for minimal unitary quantum affine W-algebras

    61. (with D. Adamovic, V. Kac and P. Moseneder Frajria),  to appear in Communications in Mathematical Physics