National Research University – Higher School of Economics

About: National Research University – Higher School of Economics is a education organization based out in Moscow, Russia. It is known for research contribution in the topics: Population & Computer science. The organization has 12873 authors who have published 23376 publications receiving 256396 citations.

Classical gravity from loop amplitudes

Abstract: The detection of gravitational waves from binary mergers such as black holes requires highly precise analytical computations as they are fed into gravitational wave templates. Employing quantum field theory methods in a post-Minkowskian expansion turns out to be a useful framework for such analytical computations. However, extracting the classical limit from the scattering amplitudes appears to be cumbersome. The authors describe an efficient method for extracting the parts of loop integrals that are needed in obtaining the classical limit.

Does “Arab Spring” Mean The Beginning Of World System Reconfiguration?

Abstract: In a previous article, “The Coming Epoch of New Coalitions: Possible Scenarios of the Near Future” (Grinin and Korotayev 2011), it was preliminarily demonstrated that the turbulent events of late 2010 and 2011 in the Arab World may well be regarded as a start of the global reconfiguration. The subsequent events have confirmed this supposition. That is why in the present article we develop this important theme. The article offers a thorough analysis of the internal conditions of Arab countries on the eve of revolutionary events, as well as causes and consequences of the Arab Revolutions. The article also offers an analysis of similar historical World System reconfigurations starting with the sixteenth-century Reformation. The analysis is based on the theory (developed by the authors) of the periodical catch-ups experienced by the political component of the World System that tends to lag behind the World System economic component. Thus, we show that the asynchrony of development of various functional subsys...

Weyl modules and q-Whittaker functions

Abstract: Let \(G\) be a semi-simple simply connected group over \(\mathbb {C}\). Following Gerasimov et al. (Comm Math Phys 294:97–119, 2010) we use the \(q\)-Toda integrable system obtained by quantum group version of the Kostant–Whittaker reduction (cf. Etingof in Am Math Soc Trans Ser 2:9–25, 1999, Sevostyanov in Commun Math Phys 204:1–16, 1999) to define the notion of \(q\)-Whittaker functions \(\varPsi _{\check{\lambda }}(q,z)\). This is a family of invariant polynomials on the maximal torus \(T\subset G\) (here \(z\in T\)) depending on a dominant weight \(\check{\lambda }\) of \(G\) whose coefficients are rational functions in a variable \(q\in \mathbb {C}^*\). For a conjecturally the same (but a priori different) definition of the \(q\)-Toda system these functions were studied by Ion (Duke Math J 116:1–16, 2003) and by Cherednik (Int Math Res Notices 20:3793–3842, 2009) [we shall denote the \(q\)-Whittaker functions from Cherednik (Int Math Res Notices 20:3793–3842, 2009) by \(\varPsi '_{\check{\lambda }}(q,z)\)]. For \(G=SL(N)\) these functions were extensively studied in Gerasimov et al. (Comm Math Phys 294:97–119, 2010; Comm Math Phys 294:121–143, 2010; Lett Math Phys 97:1–24, 2011). We show that when \(G\) is simply laced, the function \(\hat{\varPsi }_{\check{\lambda }}(q,z)=\varPsi _{\check{\lambda }}(q,z)\cdot {\prod olimits _{i\in I}\prod olimits _{r=1}^{\langle \alpha _i,\check{\uplambda }\rangle }(1-q^r)}\) (here \(I\) denotes the set of vertices of the Dynkin diagram of \(G\)) is equal to the character of a certain finite-dimensional \(G[[{\mathsf {t}}]]\rtimes \mathbb {C}^*\)-module \(D(\check{\lambda })\) (the Demazure module). When \(G\) is not simply laced a twisted version of the above statement holds. This result is known for \(\varPsi _{\check{\lambda }}\) replaced by \(\varPsi '_{\check{\lambda }}\) (cf. Sanderson in J Algebraic Combin 11:269–275, 2000 and Ion in Duke Math J 116:1–16, 2003); however our proofs are algebro-geometric [and rely on our previous work (Braverman, Finkelberg in Semi-infinite Schubert varieties and quantum \(K\)-theory of flag manifolds, arXiv/1111.2266, 2011)] and thus they are completely different from Sanderson (J Algebraic Combin 11:269–275, 2000) and Ion (Duke Math J 116:1–16, 2003) [in particular, we give an apparently new algebro-geometric interpretation of the modules \(D(\check{\lambda })]\).

Affine permutations and rational slope parking functions

Abstract: We introduce a new approach to the enumeration of rational slope parking functions with respect to the area and a generalized dinv statistics, and relate the combinatorics of parking functi ons to that of affine permutations. We relate our construction to two previously known combinatorial constructions: Haglund's bijectionexchanging the pairs of statistics (area,dinv) and (bounce,area) on Dyck paths, and the Pak-Stanley labeling of the regions of k-Shi hyperplane arrangements by k-parking functions. Essentially, our approach can be viewed as a generalization and a unification of these two constructions. We also relate o ur combinatorial constructions to representation theory. We derive new formulas for the Poincare polynomials of certain affine Springer fibers and describe a connection to the theory of finite dimensional representations of DAHA and non symmetric Macdonald polynomials.