11,255 research outputs found
Wilson lines construction of toroidal conformal blocks
No full textWe study toroidal conformal blocks for degenerate primary
fields in AdS/CFT context. In the large central charge limit
algebra reduces to algebra and blocks are
defined as contributions to blocks coming from the generators
of subalgebra. We consider the construction of
toroidal blocks in terms of Wilson lines operators of
Chern-Simons gravity in the thermal AdS space-time. According to the
correspondence, degenerate primary fields are associated with Wilson lines
operators acting in the corresponding finite-dimensional
representations. We verify this dual construction for one-point toroidal block
using tensor technique in the bulk theory and an algorithm
based on AGT correspondence in the boundary CFT
Quantum groups and Askey-Wilson polynomials
No full textIn this thesis, we introduce the quantum groups Uq(SL(2,C)) and Aq(SL(2,C)) as Hopf algebras. We study their representations, including their similarities and differences with the classical theory. We show that the eigenvectors of Koorwinder's twisted primitive elements of Uq(SU(2)) are dual q-Krawtchouk polynomials. We use this explicit expression to define generalised matrix elements and spherical functions in Aq(SL(2,C)). Then we use the Haar functional to show that these generalised matrix elements are Askey-Wilson polynomials with two continuous and two discrete parameters. Next, we show a new result. Namely, two twisted primitive elements of Uq(SL(2,C)) generate Zhedanov's Askey-Wilson algebra AW(3). Consequently, AW(3) is embedded as a subalgebra into Uq(SL(2,C)). We use this to show that overlap functions of twisted primitive elements in Uq(SU(2)) are q-Racah polynomials. With that, we derive a summation formula connecting q-Racah and dual q-Krawtchouk polynomials.Applied Mathematic
Askey-Wilson braid algebra and centralizer of
No full textA presentation of the centralizer of the three-fold tensor product of the
spin representation of the quantum group is
provided. It is expressed as a quotient of the Askey-Wilson braid algebra. This
newly defined algebra combines the Askey-Wilson relations with the braid group
relations, on three strands, together with a characteristic equation of degree
for the braid generators. Explicit bases are given for the centralizer.Comment: 23 pages, 5 figure
An Askey–Wilson Algebra of Rank 2
No full textAn algebra is introduced which can be considered as a rank 2 extension of the Askey–Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the quantum algebra Uq (sl(2, C)). It is shown that bivariate q-Racah polynomials appear as overlap coefficients of eigenvectors of generators of the algebra. Furthermore, the corresponding q-difference operators are calculated using the defining relations of the algebra, showing that it encodes the bispectral properties of the bivariate q-Racah polynomials.Analysi
Pheidole peltastes Wilson, 2003, new species
No full textPheidole peltastes new species Types Mus. Comp. Zool. Harvard. etymology Gr peltastes, soldier armed with a small shield. Diagnosis Similar to the species listed in the heading above, distinguished as follows. Major: antennal scrobes present; extensive rugoreticulum covers all the dorsal head surface from the level of the anterior margin of the eyes to the occiput, except for a median strip and the antennal scrobes. Measurements (mm) Holotype major: HW 0.54, HL 0.60, SL 0.30, EL 0.06, PW 0.32. Paratype minor: HW 0.36, HL 0.38, SL 0.30, EL 0.06, PW 0.22. color Major: body light reddish yellow ("orange"), appendages light yellow. Minor: concolorous pale yellow. Range Known only from the type locality. Biology Unknown. Figure Upper: holotype, major. Lower: paratype, minor. BRAZIL: Utinga tract, near Belem, Para (P. F. Darlington). Scale bars = 1 mm.Published as part of Wilson, E. O., 2003, Pheidole in the New World. A dominant, hyperdiverse ant genus., Cambridge, MA :Harvard University Press on page 48
Pheidole kuna Wilson, 2003, new species
No full textPheidole kuna new species Types Mus. Comp. Zool. Harvard. Etymology Kuna, Amerindian tribe of the San Bias region. Diagnosis a very small, bicolorous member of the flavens group close to flavens, with which it may be synonymous, and tayrona, distinguished from both in the major, which has a distinctive bicolorous body and angulate mesonotum. See also breviseta, hizemops, lignicola, micon, and tenebra. measurements (mm) Holotype major: HW 0.68, HL 0.74, SL 0.40, EL 0.08, PW 0.34. Paratype minor: HW 0.36, HL 0.40, SL 0.34, EL 0.06, PW 0.24. color Major and minor: gaster and postpetiole light brown; rest of body and appendages reddish yellow. Range Known only from the type series. Biology In rainforest. Figure Upper: holotype, major. Lower: paratype, minor. PANAMA: Nusagandi, San Bias Province (Leeanne E. Tennant-Alonso). Scale bars = 1 mm.Published as part of Wilson, E. O., 2003, Pheidole in the New World. A dominant, hyperdiverse ant genus., Cambridge, MA :Harvard University Press on page 44
Pheidole rectispina Wilson, 2003, new species
No full textPheidole rectispina new species Types Mus. Comp. Zool. Harvard. etymology L rectispina, upright spine. diagnosis Similar in various traits to bilimeki, floridana, hazenae, rectiluma, rectisentis, rectitrudis, sospes, and stomachosa, differing as follows. Major: propodeal spine half as long as propodeal basal face and perpendicular to it; humeri low and subangulate; mesonotal convexity present; postpetiole from above elliptical, with angulate lateral margins; all of dorsal surface of head except occipital lobes, frontal triangle, and midclypeus carinulate; all of mesosoma and most of head and waist foveolate and opaque; anterior fringe of first gastral tergite shagreened. Minor: propodeal spine half as long as the propodeal face and vertical on it; postpetiolar node somewhat depressed; occiput broad, its margin concave; all of head and mesosoma foveolate and opaque, no rugoreticulum and almost no carinulae. Measurements (mm) Holotype major: HW 1.00, HL 1.14, SL 0.56, EL 0.14, PW 0.50. Paratype minor: HW 0.44, HL 0.50, SL 0.46, EL 0.08, PW 0.30. Color Major: dark, even blackish brown. Minor: body medium brown, appendages yellowish brown. Range Atlantic slope of Costa Rica from lowlands to montane forest (Longino 1997); and Belize (Hummingbird Gap, near Stann; Stewart Peck). biology Occurs on the floor of primary rainforest. figure Upper: holotype, major. Lower: paratype, minor. COSTA RICA: La Selva Biological Station, near Puerto Viejo, Heredia (E. O. Wilson). Scale bars = 1 mm.Published as part of Wilson, E. O., 2003, Pheidole in the New World. A dominant, hyperdiverse ant genus., Cambridge, MA :Harvard University Press on page 49
Pheidole hector Wilson, 2003, new species
No full textPheidole hector new species Types iNBio. etymology Gr Hector, legendary Trojan hero. Diagnosis A large, bicolorous brown-and-yellow member of the fallax group with exceptionally long propodeal spines, especially in the minor, dense pilosity, and angulate mesonotal convexity. Similar to ajax, fiorii, jaculifera, and lourothi, differing in many details of body form, sculpturing, and pilosity, as illustrated, as well as in color. Measurements (mm) Holotype major: HW 1.54, HL 1.64, SL 1.36, EL 0.22, PW 0.78. Paratype minor: HW 0.78, HL 1.00, SL 1.46, EL 0.20, PW 0.56. color Major: body medium brown; genae anterior to eyes, as well as mandibles and tarsi, a contrasting yellow. Minor: body medium brown, legs light brown, tarsi yellow. range Known only from the type locality. Biology Under dead wood in moist forest (Longino 1997). Figure Upper: holotype, major. Lower: paratype, minor. COSTA RICA: Wilson Botanical Garden, 4 km south of San Vito, Puntarenas, 1200 m (J. T. Longino). Scale bars = 1 mm.Published as part of Wilson, E. O., 2003, Pheidole in the New World. A dominant, hyperdiverse ant genus., Cambridge, MA :Harvard University Press on page 29
Pheidole dumicola Wilson, 2003, new species
No full textPheidole dumicola new species Types Mus. Comp. Zool. Harvard. Etymology L dumicola, dweller in thorn-bush. Diagnosis Similar to charazana and floricola, differs as follows. Major: head subrectangular and moderately elongate, with straight sides; antennal scrobes present; most of anterior half of head rugoreticulate, including outer margins of frontal lobes and all of genae but not antennal fossae, frontal triangle or midclypeus; humerus in dorsal-oblique view raised and lobose; all of mesosoma foveolate; postpetiole from above spinose. Minor: pilosity sparse, with hairs on mesosomal dorsum consisting of well-spaced pairs of equal length; humerus in dorsal-oblique view subangulate; occiput broad, its margin straight; postpetiole from above large, circular, nearly 2X broader than petiole. Measurements (mm) Holotype major: HW 0.82, HL 1.00, SL 0.44, EL 0.12, PW 0.46. Paratype minor: HW 0.38, HL 0.46, SL 0.40, EL 0.06, PW 0.26. color Major and minor: light yellowish brown. Range Known only from the type locality. biology The type series, including winged reproductives, was collected from a soil nest in second-growth thorn forest, on 28-29 August 1953. Figure Upper: holotype, major. Lower: paratype, minor. MEXICO: 10 km east of Campeche, Yucatan Peninsula (E. O. Wilson). Scale bars = 1 mm.Published as part of Wilson, E. O., 2003, Pheidole in the New World. A dominant, hyperdiverse ant genus., Cambridge, MA :Harvard University Press on page 41
Pheidole laticornis Wilson, 2003, new species
No full textPheidole laticornis new species Types Mus. Comp. Zool. Harvard. etymology L laticornis, broad-horned, referring to the basally widened scape. Diagnosis A member of the diligens group close to coffeicola and vafra and differing from that species and other diligens group members by the following combination of traits. Major: scape broadened at the base, wider there than near the apex; head dark yellow, with brown spot on vertex; propodeal spines reduced to denticles. Minor: propodeal spines reduced to denticles; occiput narrowed, with nuchal collar. Other traits as illustrated. measurements (mm) Holotype major: HW 1.02, HL 1.08, SL 0.76, EL 0.18, PW 0.58. Paratype minor: HW 0.48, HL 0.60, SL 0.76, EL 0.14, PW 0.34. color Major: body and head dark yellow, with fuzzy, circular brown spot on vertex, except for gaster, which is yellowish brown. Minor: mesosoma, petiole, and appendages dark yellow; head, postpetiole, and gaster yellowish to plain light brown. range Known from the type locality and from Agua Caliente and Cartago, Costa Rica. Biology Unknown. figure Upper: holotype, major. Lower: paratype, minor. COSTA RICA: Palmar, Puntarenas (E. O. Wilson). Scale bars = 1 mm.Published as part of Wilson, E. O., 2003, Pheidole in the New World. A dominant, hyperdiverse ant genus., Cambridge, MA, USA :Harvard University Press on page 20
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