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Algimantas Adolfas Jucys


A. Jucio fotografija

the son of Professor Adolfas Jucys (born in Kaunas, Nov. 14, 1936) a Lithuanian theoretical physicist was more prominent as a mathematician. Algis Jucys graduated (1960) from the Faculty of Physics and Mathematics of Vilnius University and defended (1971) Candidate of Sc. (PhD) Thesis "Some Problems of Theory of Representations of the Groups Sn and GL(k)" (in Russian) at Vilnius University.

  • Since 1967 Algis Jucys was researcher and
  • since 1974 senior researcher at the Institute of Physics and Mathematics of Lithuanian Academy of Sciences,
  • 1977-1990 at the Institute of Physics of LithAS
  • and 1990-1996 senior researcher at the Institute of Theoretical Physics and Astronomy.

Algis Jucys was member of Lithuanian Physical Society, Lithuanian Mathematical Society, American Mathematical Society. A. Jucys died on July 29, 1997.


Algis Jucys studied the Group theoretical methods of Physics relevant to the shell models of atom and nucleus. His investigations of the representation theory of the symmetric (permutation) group Sn and the full linear group GL(k) (and unitary U(k) group) based on the Schur–Weyl duality between Sn and GL(k) were appreciated after he introduced (in 1974) special elements Xi = (1 i) + (2 i) + . . . + (i − 1 i), i = 1, 2, . . . , n; X0 = 0, X1 = (1, 2), . . . ( where (j i) is a permutation of j and i) of the centre of Sn group algebra as an important tool of the representation theory of Sn . Although this result remained unnoticed for some time, an English mathematician G. Murphy in 1981 rediscovered these elements (later denoted by algebraists as the Jucys–Murphy elements) and then found paper by Jucys. The Young or Gelfand–Tsetlin (GZ) basis for irreducible representations of Sn is formed by the eigenstates of the Jucys–Murphy elements. The action of Sn generators Pk=(k k+1) in the space of irreducible representations can be easily deduced from the obvious relations PiXj= XjPi (unless j= i, i + 1) and a more interesting (and well-known) relation PiXi + 1 = Xi+1Pi . Hence, the Jucys-Murphy elements are widely used in the representation theory of Sn (see, for example, arXiv:math.RT/0503040) and are extended for the Coxeter groups (which include the symmetric groups), braid groups, affine Hecke algebras. They are also widely used in problems of the contemporary mathematical physics relevant to the solution of the quantum inverse scattering problem, the Yang-Baxter equation, investigations of quantum groups and different exactly solvable and integrable systems of statistical physics.

Because many original works of A. A. Jucys were published in Lithuanian and Russian journals, most of which are unavailable today, this page is intended to fill the gap. The web site include scanned copies of his papers in Djvu format.

A. A. Jucys publication list

  1. V.V. Vanagas, А.A. Jucys, "О коэффициентах Клебша-Гордана группы унитарных матриц третьего порядка", Lietuvos fiz. rinkinys – Litov. fiz. sb., 2, No. 3-4, p. 199-211, 1962; English summ.
  2. А.А. Jucys, "Об операторах Юнга симметрических групп" (On the Young operators of the symmetric groups), Liet. fiz. rink. – Litov. fiz. sb., 6, No. 2, p. 163-180, 1966
  3. А.А. Jucys, V.V. Vanagas, R.I. Rakauskas "Энергетический спектр основной конфигураций ядер O18 и F18 в модели оболочек", Liet. fiz. rink. – Litov. fiz. sb., 6, No. 2, p. 201-206, 1966
  4. А.А. Jucys, "Представления симметрических групп и коэффициенты Клебша-Гордaна унитарных групп" (Representations of the symmetric groups and the Clebsch-Gordan coefficients of the unitary groups), Lietuvos matem. rinkinys – Litov. matem. sb. (Lithuanian mathematical journal), 8, No. 3, p. 597-609, 1968; English summ.
  5. А.A. Jucys, "Представления симметрических групп и матрицы преобразования унитарных групп" (Representations of the symmetric groups and recoupling coefficients for the unitary groups), Liet. fiz. rink. – Litov. fiz. sb., 9, No. 4, p. 629-639, 1969; English summ.
  6. А.A. Jucys,"Об изоскалярных множителях коеффициентов Клебша-Гордaна унитарных групп", Liet. fiz. rink. – Litov. fiz. sb., 10, No. 1, p. 5-12, 1970
  7. А.A. Jucys, "Условия унитарности для матрицы, приводящeй представление конечной группы", Liet. fiz. rink. – Litov. fiz. sb., 10, No. 5, p. 669-673, 1970
  8. А.A. Jucys, "Факторизация проекционных операторов Юнга симметрических групп" (Factorization of Young projection operators for the symmetric group), Liet. fiz. rink. – Litov. fiz. sb., 11, No. 1, p. 5-10, 1971
  9. S.J. Ališauskas, A.P. Jucys, А.A. Jucys, "On the symmetric tensor operators of the unitary groups", J. Math, Phys., 13, No. 9, p. 1329-1333, 1972
  10. А.А. Jucys, "Symmetric polynomials and the center of the symmetric group ring", Rep. Math, Phys., 5, No. 1, 107-112, 1974
  11. А.А. Jucys, "The number of distinct Latin squares as a group theoretical constant", J. Combinatorial Theory, 20, No. 3, p. 265-272, 1976. Abstract
  12. А.А. Jucys, "Характеры групп и некоторые задачи перечисления в комбинаторном анализе", Liet. matem. rink. – Lit. matem. sb. (Lith. Math. J.) , 16, No. 2, p. 189-190, 1976
  13. A.A. Jucys, "A note on one conjecture", (unpublished, on the intertwining numbers of irred. representations of SN and Sn'×Sn''×...×Sn in the form of diophantine equations)
  14. А.А. Jucys, "Число симметрических целочисленных матриц с заданнымии суммами элементов в строках", Liet. matem. rink. – Lit. matem. sb., 17, No. 1, p. 205-208, 1977; " The number of symmetric nonnegative integral matrices with prescribed row sums", Lithuanian mathematical journal , 17, No. 1, p. 137-139, 1977
  15. A.A. Jucys, L. B. Sabaliauskas, A. P. Bernotas, "Классификация SU(3) состояний для нечётных тяжелых ядер", Liet. fiz. rink. – Litov. fiz. sb., 20, No. 1, p. 3-13, 1980; "Classification of SU(3)-states for odd heavy nuclides", Sov. Phys. Collection (Lit. fiz. sb.), 20, No. 1, 1-8, 1980.
  16. A.A. Jucys, A. P. Bernotas, "Подпрограмма расчёта прямой и обратной матриц Костки", Алгоритмы и программы , 1, No. 77, 1980
  17. А.А. Jucys, "Турниры и обобщённые таблицы Юнга", Математические заметки, 23, No. 3, p. 353-358, 1980
  18. A.А. Jucys, "Представления симметрических групп и построение неканонических базисов представлений в сужении групп Uk(k+1)/2 ⊃ Uk", in Group theoretical methods in physics, Proceedings of international seminar, Zvenigorod, Vol.2, pp. 508-512, "Nauka", M. 1983
  19. А.A. Jucys, "Symmetric group representations and noncanonical bases in subduction Uk(k+1)/2 ⊃Uk", in Group-theoretical methods in physics, Proceed. of International Seminar, Zvenigorod, 1982, Eds. M. Markov, V. Man’ko (Harwood Acad. Publ., Chur, London, Paris), Vol. 1, pp. 61-65, 1985.
  20. А.А. Jucys, A.B. Bičkutė, "Предстaвления симметрических групп на множестве разбиений", XXIV conference of Lithuanian mathematical society, Vilnius state university publisher, p. 330-331, 1984, Vilnius
  21. A.А. Jucys, "Разбиения на ограниченные части. Кратность термов оболочек эквивалентных частиц", Liet. fiz. rink. – Litov. fiz. sb., 23, No. 5, p. 105-107, 1983; "Partitions into limited parts: multiplicities of terms of shells of equivalent particles", Sov. Phys. Collection (Lit. fiz. sb.), 23, No. 5, p. 80-82, 1983
  22. A.А. Jucys, "Кратности представлений в ограничении групп", Liet. fiz. rink. – Litov. fiz. sb., 25, No. 2, p. 3-9, 1985; Correction, ibid, 26, p. 507, 1986
  23. А.А. Jucys, "Рекурpентные соотношения для характеров линейных и симметрических групп", XXVI conference of Lithuanian mathematical society, Published by Institute of mathematics and cybernetics, p. 310-311, 1985, Vilnius
  24. A.А. Jucys, "Задача, обобщающая задачу перечисления разбиений. Кратности представлений симметрических групп", Liet. fiz. rink. – Litov. fiz. sb., 26, No. 5, 513-526, 1986; "The problem of multiplicity of symmetrical group representation which generalizes the problem of partition numbering", Sov. Phys. Collection (Lit. fiz. sb.), 26, No. 5, 1-13, 1986
  25. А.А. Jucys, "Плетизм и кратности представлений симметрических групп", XXVII conference of Lithuanian mathematical society, Vilnius state university publisher, p. 32-33, 1986, Vilnius
  26. А.A. Jucys, "О числе решений линейного диофантова уравнения", XII school on the operator theory in functional spaces , Part. 2, p. 128, 1987, Tambov
  27. А.А. Jucys, "Заметка о внутреннем произведении функций Шура", Liet. matem. rink. – Lit. matem. sb., 27, No. 4, 793-797, 1987; "Inner Product of Schur Functions", Lithuanian Math. J., 27, No. 4, 375-378, 1987
  28. A.А. Jucys, "Алгебра подклассов конечной группы", Liet. fiz. rink. – Litov. fiz. sb., 27, No. 4, p. 391-402, 1987; "Subclass Algebra of a Finite Group", Sov. Phys. Collection (Lit. fiz. sb.), 27, No. 4, p. 1-10, 1987
  29. А.А. Jucys, "Об амбивалентных подклассах конечной группы", XXVIII conference of Lithuanian mathematical society, p. 382-383, 1987
  30. А.A. Jucys, "Kinta elementarusis elektros krūvis?" (popular. str.), Mokslas ir technika, No. 2 1987
  31. A.А. Jucys, "Представления симметрической группы в пространстве многочленов. Кратности квантовых состояний в моделях независимых частиц", Liet. fiz. rink. – Litov. fiz. sb., 29, No. 3, p. 267-274, 1989
  32. A.A. Jucys, "Представления симметрической группы в фактор-кольце кольца многочленов по симметрическим многочленам", XXIX conference of Lithuanian mathematical society, p. 126-127, 1988, Vilnius
  33. A.A. Jucys, V. L. Gineitytė, "Изучение зонной структуры спектров одноэлектронных энергий насыщеных систем", (unpublished)
  34. A.A. Jucys, "Общее алгебраическое решение модельной спектральной задачи с четырнадцатью параметрами для n-алканов", (unpublished)
  35. A.А. Jucys, "Производящие функции, алгоритм Шенстеда и индексы интенсивности перестановок", Liet. fiz. žurn., 35, No. 1, p. 3-6, 1995; Generating functions, Schensted algorithm and quater indices of permutations, Lith. Phys. J., 35, No. 1, p. 3-5, 1995
  36. A.А. Jucys, "The bijection between plane partitions and nonnegative integer matrices", Liet. Matem. Rink., 35, No. 2, p. 204-210, 1995

This page last updated by Artūras Acus on April 26, 2005. Bibliography sources collected and verified by Sigitas Ališauskas