Entry strategy concepts, determinants and options of US firms into Romania

This article looks at entry strategy concepts and options, taking into account cultural and organizational parameters which influence success. Export, licensing and distribution, as well as joint ventures and facilities management are critically examined, from the point of view of the foreign companies intending to access Romanian market.strategic marketing, entry strategies, US companies, Romanian market.

The innovation misstep

The author makes the case that cause of innovation to battle commoditization is far too often lost even before it starts. The dysfunctional distribution system has been turned on its head as distributors have wrested control of the strategic prerogatives of manufacturers in order to capture a disproportionate share of the value of the supplying company’s products. Mega distributors like Wal-Mart Stores Inc. and Home Depot Inc. end up profiting at the expense of their vendors, and manufacturers earn little or nothing on the sale of their own innovated products. The mega distributors not only control the delivery of their products to consumers but also wield tremendous power over their internal processes, further reducing the value of the innovation. There is some hope: if done right, manufacturers still possess the ability to directly influence what happens to their innovations products once they enter the distribution chain, but, this window is rapidly closing.innovation management; sales and distribution strategy; direct marketing; channel control.

A commutant realization of Odake's algebra

The bc\beta\gamma-system W of rank 3 has an action of the affine vertex algebra V_0(sl_2), and the commutant vertex algebra C =Com(V_0(sl_2), W) contains copies of V_{-3/2}(sl_2) and Odake's algebra O. Odake's algebra is an extension of the N=2 superconformal algebra with c=9, and is generated by eight fields which close nonlinearly under operator product expansions. Our main result is that V_{-3/2}(sl_2) and O form a Howe pair (i.e., a pair of mutual commutants) inside C. More generally, any finite-dimensional representation of a Lie algebra g gives rise to a similar Howe pair, and this example corresponds to the adjoint representation of sl_2.Comment: Minor corrections, discussion of Odake's algebra in Section 2 expanded, final versio

Cosets of the Wk(sl4,fsubreg)\mathcal{W}^k(\mathfrak{sl}_4, f_{\text{subreg}})-algebra

Let $\mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}})$ be the universal $\mathcal{W}$-algebra associated to $\mathfrak{sl}_4$ with its subregular nilpotent element, and let $\mathcal {W}_k(\mathfrak{sl}_4, f_{\text {subreg}})$ be its simple quotient. There is a Heisenberg subalgebra $\mathcal{H}$, and we denote by $\mathcal{C}^k$ the coset $\text{Com}(\mathcal{H}, \mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}}))$, and by $\mathcal{C}_k$ its simple quotient. We show that for $k=-4+(m+4)/3$ where $m$ is an integer greater than $2$ and $m+1$ is coprime to $3$, $\mathcal{C}_k$ is isomorphic to a rational, regular $\mathcal W$-algebra $\mathcal{W}(\mathfrak{sl}_m, f_{\text{reg}})$. In particular, $\mathcal{W}_k(\mathfrak{sl}_4, f_{\text {subreg}})$ is a simple current extension of the tensor product of $\mathcal{W}(\mathfrak{sl}_m, f_{\text{reg}})$ with a rank one lattice vertex operator algebra, and hence is rational.Comment: 14 pages, to appear in conference proceedings for AMS Special Session on Vertex Algebras and Geometr

Orbifolds of symplectic fermion algebras

We present a systematic study of the orbifolds of the rank $n$ symplectic fermion algebra $\mathcal{A}(n)$, which has full automorphism group $Sp(2n)$. First, we show that $\mathcal{A}(n)^{Sp(2n)}$ and $\mathcal{A}(n)^{GL(n)}$ are $\mathcal{W}$-algebras of type $\mathcal{W}(2,4,\dots, 2n)$ and $\mathcal{W}(2,3,\dots, 2n+1)$, respectively. Using these results, we find minimal strong finite generating sets for $\mathcal{A}(mn)^{Sp(2n)}$ and $\mathcal{A}(mn)^{GL(n)}$ for all $m,n\geq 1$. We compute the characters of the irreducible representations of $\mathcal{A}(mn)^{Sp(2n)\times SO(m)}$ and $\mathcal{A}(mn)^{GL(n)\times GL(m)}$ appearing inside $\mathcal{A}(mn)$, and we express these characters using partial theta functions. Finally, we give a complete solution to the Hilbert problem for $\mathcal{A}(n)$; we show that for any reductive group $G$ of automorphisms, $\mathcal{A}(n)^G$ is strongly finitely generated.Comment: Exposition streamlined, some new results added in Section 5, references added. arXiv admin note: text overlap with arXiv:1205.446

Cosets of affine vertex algebras inside larger structures

Given a finite-dimensional reductive Lie algebra $\mathfrak{g}$ equipped with a nondegenerate, invariant, symmetric bilinear form $B$, let $V^k(\mathfrak{g},B)$ denote the universal affine vertex algebra associated to $\mathfrak{g}$ and $B$ at level $k$. Let $\mathcal{A}^k$ be a vertex (super)algebra admitting a homomorphism $V^k(\mathfrak{g},B)\rightarrow \mathcal{A}^k$. Under some technical conditions on $\mathcal{A}^k$, we characterize the coset $\text{Com}(V^k(\mathfrak{g},B),\mathcal{A}^k)$ for generic values of $k$. We establish the strong finite generation of this coset in full generality in the following cases: $\mathcal{A}^k = V^k(\mathfrak{g}',B')$, $\mathcal{A}^k = V^{k-l}(\mathfrak{g}',B') \otimes \mathcal{F}$, and $\mathcal{A}^k = V^{k-l}(\mathfrak{g}',B') \otimes V^{l}(\mathfrak{g}",B")$. Here $\mathfrak{g}'$ and $\mathfrak{g}"$ are finite-dimensional Lie (super)algebras containing $\mathfrak{g}$, equipped with nondegenerate, invariant, (super)symmetric bilinear forms $B'$ and $B"$ which extend $B$, $l \in \mathbb{C}$ is fixed, and $\mathcal{F}$ is a free field algebra admitting a homomorphism $V^l(\mathfrak{g},B) \rightarrow \mathcal{F}$. Our approach is essentially constructive and leads to minimal strong finite generating sets for many interesting examples. As an application, we give a new proof of the rationality of the simple $N=2$ superconformal algebra with $c=\frac{3k}{k+2}$ for all positive integers $k$.Comment: Some errors corrected, final versio

W-algebras as coset vertex algebras

We prove the long-standing conjecture on the coset construction of the minimal series principal $W$-algebras of $ADE$ types in full generality. We do this by first establishing Feigin's conjecture on the coset realization of the universal principal $W$-algebras, which are not necessarily simple. As consequences, the unitarity of the "discrete series" of principal $W$-algebras is established, a second coset realization of rational and unitary $W$-algebras of type $A$ and $D$ are given and the rationality of Kazama-Suzuki coset vertex superalgebras is derived.Comment: Minor corrections and typos fixed. Proposition 3.4 is strengthened, which simplifies the proofs of Lemma 5.2 and Lemma 8.1. Final version to appear in Invent. Mat