arXiv:
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[1] Kosyak A. and Albeverio S. q-Pascal's triangle and irreducible representations of the
braid group B_3 in arbitrary dimension, arXiv:math.QA(RT)/
0803.2778v2
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[2] A.V.Kosyak
Representations of the braid group $B_n$ and the highest weight
modules of $U(\mathfrak{sl}_{n-1})$ and
$U_q(\mathfrak{sl}_{n-1})$, arXiv:math.QA(RT)/
0803.2785v2.
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[3] A.V. Kosyak, Type III_1 factors generated by regular representations of
infinite dimensional nilpotent group $B_0^{\mathbb N}$,
arXiv:math.RT(OA)/
0803.3340v1
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[4] A.V.Kosyak, Irreducibility criterion for the set of two matrices.
arXiv:math.RT(GR)/0807.4696.
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Journals:
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[1] Albeverio, Sergio; Kosyak, Alexandre,
Quasiregular
representations of the infinite-dimensional nilpotent group,
J.Funct. Anal. 236 (2006) 634-681.
pdf
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[2] Kosyak, A. V.; Nizhnik, L. P. Generalized translation
operators and hypergroups constructed from selfadjoint
differential operators. (Russian) Ukr. Mat. Zh. 57
(2005), no. 5, 659--668; translation in Ukrainian Math. J. 57
(2005), no. 5, 782--793.
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[3] Albeverio, Sergio; Kosyak, Alexandre, Group action,
quasi-invariant measures and quasiregular representations of the
infinite-dimensional nilpotent group. Algebraic and topological
dynamics, 259--280, Contemp. Math., 385, Amer. Math. Soc.,
Providence, RI, 2005.
pdf
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[4] Albeverio, Sergio; Kosyak, Alexandre, Quasiregular
representations of the infinite-dimensional Borel group. J. Funct.
Anal. 218 (2005), no. 2, 445--474.
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[5] Kosyak, A. V. Quasi-invariant measures and irreducible
representations of the inductive limit of special linear groups.
(Russian) Funktsional. Anal. i Prilozhen. 38 (2004), no. 1,
82--84; translation in Funct. Anal. Appl. 38 (2004), no. 1,
67--68.
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[6] Kosyak, Alexandr; Zekri, Richard, Anti-Wick symbols for
infinite products in $K$-homology. $K$-Theory 29 (2003), no. 2,
117--145.MR2029758 (2005d:46149)
pdf
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[7] Kosyak, A. V. A critierion for the irreducibility of
quasiregular representations of the group of finite
upper-triangular matrices. (Russian) Funktsional. Anal. i
Prilozhen. 37 (2003), no. 1, 78--81; translation in Funct. Anal.
Appl. 37 (2003), no. 1, 65--68. MR1988011 (2004f:22021)
pdf
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[8] Kosyak, O. V. Elementary representations of the group $B\sb
0\sp {\Bbb Z}$ of infinite in both directions upper-triangular
matrices. I. Ukrai"n. Mat. Zh. 54 (2002), no. 2, 205--215;
translation in Ukrainian Math. J. 54 (2002), no. 2, 253--265. MR1952821 (2004a:28028)
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[9] Kosyak, A. V.; Leandr, R. Regular representations of the
central extension of the diffeomorphism group of the circle.
(Russian) Dokl. Akad. Nauk 385 (2002), no. 4, 453--455.
MR1944075
pdf
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[10] Kosyak, A. V. The generalized Ismagilov conjecture for the
group $B\sb 0\sp \Bbb N$. II. Methods Funct. Anal. Topology 8
(2002), no. 3, 27--45. MR1926911 (2003k:22027)
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[11] Kosyak, A. V. The generalized Ismagilov conjecture for the
group $B\sb 0\sp {\Bbb N}$. I. Methods Funct. Anal. Topology 8
(2002), no. 2, 33--49. MR1922683 (2003f:22025)
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[12] Kosyak, A. V. Elementary representations of the group $B\sb
0\sp {\Bbb N}$ of finite upper-triangular matrices. I. Methods
Funct. Anal. Topology 7 (2001), no. 1, 34--44. MR1909906 (2003e:22011)
dvi |
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[13] Kosyak, A. V. Irreducibility of regular Gaussian
representations of the group $B\sb 0\sp {\Bbb Z}$. Methods Funct.
Anal. Topology 7 (2001), no. 2, 42--51. MR1909687 (2003e:22012)
dvi
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[14] Kosyak, A. V.; Zekri, R. Regular representations of
infinite-dimensional group $B\sp {\Bbb Z}\sb 0$ and factors.
Methods Funct. Anal. Topology 7 (2001), no. 4, 43--48.
MR1879484 (2002k:22005) |
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[15] Kosyak, A. V. Regular representations of the group of finite
upper-triangular matrices, corresponding to product measures, and
criteria for their irreducibility. Methods Funct. Anal. Topology 6
(2000), no. 4, 43--55. MR1819617 (2002a:22025)
dvi
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[16] Kosyak, A. V.; Zekri, R. Regular representations of
infinite-dimensional groups and factors. I. Methods Funct. Anal.
Topology 6 (2000), no. 2, 50--59. MR1783774 (2001h:46116)
dvi
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[17] Kosyak, A. V. Gaussian measures, quasi-invariant with respect
to inverse transformations, on the group of upper-triangular
matrices of infinite order. (Russian) Funktsional. Anal. i
Prilozhen. 34 (2000), no. 1, 86--90; translation in Funct. Anal.
Appl. 34 (2000), no. 1, 70--72. MR1756739 (2001j:28013)
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[18] Kosyak, Alexandr; Zekri, Richard Anti-Wick symbols on
infinite tensor product spaces. Methods Funct. Anal. Topology 5
(1999), no. 2, 29--39.
MR1771898 (2001e:46121) |
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[19] Kosyak, A. V. Measures on infinite-dimensional groups,
quasi-invariant with respect to inverse mapping and the commutant
theorem. Analysis on infinite-dimensional Lie groups and algebras
(Marseille, 1997), 182--196, World Sci. Publishing, River Edge,
NJ, 1998. MR1743167 (2001f:22062)
www
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[20] Kosyak, A. V. Irreducible regular Gaussian representations
of the groups of the interval and circle diffeomorphisms. J.
Funct. Anal. 125 (1994), no. 2, 493--547. MR1297679 (95j:22026)
pdf
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[21] Kosyak, A. V. Criteria for irreducibility and equivalence of
regular Gaussian representations of groups of finite
upper-triangular matrices of infinite order. Selected
translations. Selecta Math. Soviet. 11 (1992), no. 3, 241--291.MR1181263 (93i:22024)
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[22] Kosyak, A. V.; Samoilenko, Yu. S. Quasi-invariant
measures on "large" groups [translation of The spectral theory of
operator-differential equations (Russian), 64--69, Akad. Nauk
Ukrain. SSR, Inst. Mat., Kiev, 1986; MR0893011 (88g:60024)].
Selected translations. Selecta Math. Soviet. 10 (1991), no. 1,
1--6.
MR1099431 |
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[23] Kosyak, A. V. A criterion for the irreducibility and
equivalence of regular Gaussian representations of the group of
finite upper-triangular matrices of infinite order. (Russian)
Akad. Nauk Ukrain. SSR Inst. Mat. Preprint 1990, no. 50, 55 pp. MR1124490
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[24] Kosyak, A. V. A criterion for irreducibility of regular
Gaussian representations of the group of finite upper-triangular
matrices. (Russian) Funktsional. Anal. i Prilozhen. 24 (1990), no.
3, 82--83; translation in Funct. Anal. Appl. 24 (1990), no. 3,
243--245 (1991). MR1082042 (91m:20016)
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[25] Kosyak, A. V. Extension of unitary representations of
inductive limits of finite-dimensional Lie groups. Rep. Math.
Phys. 26 (1988), no. 2, 285--302. MR0991725 (90d:22025)
pdf
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[26] Kosyak, A. V.; Samoilenko, Yu. S. Quasi-invariant
measures on "large" groups. (Russian) The spectral theory of
operator-differential equations (Russian), 64--69, iv, Akad. Nauk
Ukrain. SSR, Inst. Mat., Kiev, 1986.
MR0893011 (88g:60024) |
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[27] Kosyak, A. V. Extension of unitary representations of a
group of finite upper-triangular matrices of infinite order.
(Russian) Spectral theory of operators and infinite-dimensional
analysis, 102--111, iv, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev,
1984.
MR0817223 (87g:22022) |
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[28] Kosyak, A. V. The Garding domain for representations of
canonical commutation relations. (Russian) Ukrain. Mat. Zh. 36
(1984), no. 6, 709--715.
MR0772544 (87h:81080) |
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[29] Kosyak, A. V.; Samoilenko, Yu. S. The Garding domain
and entire vectors for inductive limits of commutative locally
compact groups. (Russian) Ukrain. Mat. Zh. 35 (1983), no. 4,
427--434. MR0712461 (85g:22009)
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[30] Kosyak, A. V. Analytic and entire vectors for families of
operators. (Russian) Spectral analysis of differential operators,
pp. 3--18, 132, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1980.
MR0642526 (83f:47021) |
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[31] Kosjak, A. V.; Samoilenko, Ju. S. Families of commuting
selfadjoint operators. (Russian) Ukrain. Mat. Zh. 31 (1979), no.
5, 555--558. MR0552491 (80m:47023)
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